JEE Main Previous Year Questions (2021-23): Current Electricity PDF Download

Q.1. As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3Ω. The currents through the resistors R₄ and R₅ are I₄ and I₅ respectively. The values of I₄ and I₅ are:         [JEE Main 2023]
(a)
(b)
(c)
(d)

Ans. a

Q.2. A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n  × 10⁻³Ω. If the resistivity of the material is 2.4 × 10⁻⁸Ωm. The value of n is           [JEE Main 2023]

Ans. 2

Q.3. A cell of emf 90 V is connected across series combination of two resistors each of 100Ω resistance. A voltmeter of resistance 400Ω is used to measure the potential difference across each resistor. The reading of the voltmeter will be:          [JEE Main 2023]
(a) 90 V
(b) 45 V
(c) 80 V
(d) 40 V

Ans. b
as Resistance are same so equal division of potential.
∴ 90/2 = 45 V

Q.4. If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is _________ %          [JEE Main 2023]

Ans. 44
Length becomes = 1.2 times
ℓ' = 1.2ℓ
R ' = n² R
= (1.2 )² R
= 1.44 R
ΔR = 0.44 R

Q.5. Three identical resistors with resistance R = 12Ω and two identical inductors with self inductance L = 5mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _______ A.          [JEE Main 2023]

Ans. 3
Short all inductor
Req. = R/3 = 12/3 = 4Ω
I = 12/4 = 3A

Q.6. A1 m long wire is broken into two unequal parts X and Y. The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y. [JEE Main 2022]
(a) 1 : 4
(b) 1 : 2
(c) 4 : 1
(d) 2 : 1

Ans. b
When wire is stretched to double of its length, then resistance becomes 4 times

So,

Q.7. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.[JEE Main 2022]
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is NOT the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Ans. a
Since they have low temperature coefficient of resistance, their resistance remains almost constant.

Q.8. Two metallic wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the these wires respectively, the effective conductivity of the combination is : [JEE Main 2022]

(a)
(b)
(c)
(d)

Ans. b
R = R₁ + R₂
⇒
⇒
⇒

Q.9. Given below are two statements : [JEE Main 2022]
Statement I : A uniform wire of resistance 80Ω is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5Ω.
Statement II: Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3:2.
In the light of the above statements, choose the most appropriate answer from the option given below
(a) Both statement I and statement II are correct
(b) Both statement I and statement II are incorrect
(c) Statement I is correct but statement II is incorrect
(d) Statement I is incorrect but statement II is correct

Ans. c
Statement I : 
⇒
Statement II : 
= 2/3

Q.10. A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :[JEE Main 2022]
(a) 9 : 1
(b) 1 : 9
(c) 4 : 1
(d) 3 : 1

Ans. a

Q.11. (A) The drift velocity of electrons decreases with the increase in the temperature of conductor.[JEE Main 2022]
(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.
(C) The drift velocity does not depend on the applied potential difference to the conductor.
(D) The drift velocity of electron is inversely proportional to the length of the conductor.
(E) The drift velocity increases with the increase in the temperature of conductor.
Choose the correct answer from the options given below :
(a) (A) and (B) only
(b) (A) and (D) only
(c) (B) and (E) only
(d) (B) and (C) only

Ans. b
V_d decreases with increase in temperature and V_d is inversely proportional to the area of cross section. 

Q.12. Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are r₁ and r₂ (r₁>r₂). If the potential difference across the source of internal resistance r₁ is zero, then the value of R will be:  
[JEE Main 2022]
(a) r₁ - r₂
(b)
(c)
(d) r₂ - r₁

Ans. a

⇒ R = r₁ - r₂

Q.13. A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery is :[JEE Main 2022]
(a) 1A
b) 2A
(c) 6/11 A
(d) 4/3 A

Ans. a
Balance wheatstone
⇒ R_eff = 3 x 6 / 3 + 6 x 2 + 2
= 6 Ω
⇒ I = V/R = 1 A

Q.14. The current I in the given circuit will be : [JEE Main 2022]
(a) 10 A
(b) 20 A
(c) 4 A
(d) 40 A

Ans. a
So, R_net = 4Ω
So, i = V / R_{net = 10 A}

Q.15. A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be: [JEE Main 2022]
(a) 50 V
(b) 75 V
(c) 150 V
(d) 275 V

Ans. d
Effective =
=
⇒
=275 V

Q.16. Which of the following physical quantities have the same dimensions? [JEE Main 2022]
(a) Electric displacement and surface charge density
(b) Displacement current and electric field
(c) Current density and surface charge density
(d) Electric potential and energy

Ans. a
Electric displacement

[Surface charge density] = [Q] / [A]
[σ] = [ATL⁻²]
⇒  and [σ] have same dimensions

Q.17. An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 Ω. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be : [JEE Main 2022]
(a) 9 Ω
(b) 18 Ω
(c) 28 Ω
(d) 126 Ω

Ans. b
Initially, copper wire radius (r₁) = 9 mm
Resistance (R) = 14 Ω
We know,
Now this copper wire is replaced by 7 parallel copper wire of resistance R₁.
∴ Equivalent resistance of 7 parallel copper wire,

= 18 Ω

Q.18. Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance 20 Ω. A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is : [JEE Main 2022]
(a) 2.5 Ω
(b) 4 Ω
(c) 5 Ω
(d) 10 Ω

Ans. c

⇒ r = 5Ω

Q.19. What will be the most suitable combination of three resistors A = 2Ω, B = 4Ω, C = 6Ω so that (22/3)Ω is equivalent resistance of combination? [JEE Main 2022]
(a) Parallel combination of A and C connected in series with B.
(b) Parallel combination of A and B connected in series with C.
(c) Series combination of A and C connected in parallel with B.
(d) Series combination of B and C connected in parallel with A.

Ans. b

⇒ A and B are in parallel and C is in series.

Q.20. A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for 1/3 deflection in the galvanometer. Which of the below is true for measuring value of G? [JEE Main 2022]
(a) 1/3 deflection method cannot be used for determining the resistance of the galvanometer.
(b) 1/3 deflection method can be used and in this case the G equals to twice the value of shunt resistances.
(c) 1/3 deflection method can be used and in this case, the G equals to three times the value of shunt resistances.
(d) 1/3 deflection method can be used and in this case the G value equals to the shunt resistances.

Ans. b
The circuit for the given situation is:
Since G and S are in parallel,
⇒
⇒ G = 2S
⇒ G equals twice the value of shunt resistance.

Q.21. In the figure, a very large plane sheet of positive charge is shown. P₁ and P2 are two points at distance l and 2l from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields E₁ and E₂ at P₁ and P₂ respectively are :  
[JEE Main 2022]
(a) E₁ = σ/ε₀,E² = σ/2ε₀
(b) E₁ = 2σ/ε₀,E² = σ/ε₀
(c) E₁ = E₂ = σ/2ε₀
(d) E₁ = E₂ = σ/ε₀

Ans. c
For an infinite charged plane
E = σ / 2ε₀ for any value of l
⇒ E₁ = E₂ = σ / 2ε₀

Q.22. If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then the total current I when its figure of merit is K will be: [JEE Main 2022]
(a)
(b)
(c)
(d)

Ans. d
According to the information, current through galvanometer = nK

Q.23. Two cells of same emf but different internal resistances r₁ and r₂ are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is : [JEE Main 2022]
(a) r₂ − r₁
(b) r₁ − r₂
(c) r₁
(d) r₂

Ans. a

As per the question,

⇒ R = r₂ - r₁

Q.24. The equivalent resistance between points A and B in the given network is :
[JEE Main 2022]
(a) 65Ω
(b) 20Ω
(c) 5Ω
(d) 2Ω

Ans. c
Initially 5 Ω and 5 Ω are in series and then in parallel with 10 Ω this pattern continues thus
R_net = 5

Q.25. An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is : [JEE Main 2022]
(a) 0.4%
(b) 0.2%
(c) 0.8%
(d) 0.6%

Ans. c

Also volume will remain constant 
i.e., Al = constant
⇒ A ∝ 1 / l
∴ R ∝ l²

Q.26. A 72 Ω galvanometer is shunted by a resistance of 8 Ω. The percentage of the total current which passes through the galvanometer is :[JEE Main 2022]
(a) 0.1%
(b) 10%
(c) 25%
(d) 0.25%

Ans. b
From the given setup
y × R_G = (x − y)(RS)
⇒ y × 72 = (x − y) × 8
⇒ 9y = x − y
⇒ y = x/10 or 10% of x

Q.27. Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).
A charge particle of 3π coulomb is passing through the point P with velocity  m/s where  and   represents unit vector along x & y axis respectively. The force acting on the charge particle is N. The value of x is : [JEE Main 2022]
(a) 2
(b) 1
(c) 3
(d) -3

Ans. c
Field at P is
=
=
So, Force

x = 3

Q.28. Resistance of the wire is measured as 2 Ω and 3 Ω at 10^∘C and 30^∘C respectively. Temperature co-efficient of resistance of the material of the wire is : [JEE Main 2022]
(a) 0.033^∘C⁻¹
(b) −0.033^∘C⁻¹
(c) 0.011^∘C⁻¹
(d) 0.055^∘C⁻¹

Ans. a
R₁₀ = 2 = R₀(1 + α × 10)
R₃₀ = 3 = R₀(1 + α × 30)
On solving
α = 0.033/^∘C

Q.29. The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2Ω. The value of internal resistance of each cell is [JEE Main 2022]
(a) 2Ω
(b) 4Ω
(c) 6Ω
(d) 8Ω

Ans. a
From diagram

given i_p = i_s

r = 2Ω

Q.30. The current I flowing through the given circuit will be __________A. [JEE Main 2022]

Ans. 2
All 9 Ω resistances are in parallel
R_eq = 3Ω
I = 6/3A = 2A

Q.31. An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _______ W. [JEE Main 2022]

Ans. 14

This power developed is proportional to resistance.
So,

Q.32. As shown in the figure, a potentiometer wire of resistance 20Ω and length 300 cm is connected with resistance box (R.B.) and a standard cell of emf 4 V. For a resistance 'R' of resistance box introduced into the circuit, the null point for a cell of 20mV is found to be 60 cm. The value of 'R' is ___________ Ω. [JEE Main 2022]

Ans. 780

20 + R = 800
R=780Ω

Q.33. In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be ______________ cm. [JEE Main 2022]

Ans. 40
Even if the radius of wire is doubled, the balancing point would not change as , which is not including a term of area.

Q.34. A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is 2.0 mm² and the resistivity of copper is 1.7×10⁻⁸Ωm, the force experienced by moving electron in the wire is ____________ ×10⁻²³ N.
(charge on electorn =1.6 × 10⁻¹⁹C) [JEE Main 2022]

Ans. 136

=136 × 10⁻²³ N

Q.35. In a meter bridge experiment, for measuring unknown resistance 'S', the null point is obtained at a distance 30 cm from the left side as shown at point D. If R is 5.6 kΩ, then the value of unknown resistance 'S' will be __________ Ω. [JEE Main 2022]

Ans. 2400
R/S = 70/30
S = 3/7 x 5.6 x 10³  = 2.4 x 10³Ω
= 2400Ω

Q.36. A potentiometer wire of length 300 cm is connected in series with a resistance 780 Ω and a standard cell of emf 4V. A constant current flows through potentiometer wire. The length of the null point for cell of emf 20mV is found to be 60 cm. The resistance of the potentiometer wire is ____________ Ω. [JEE Main 2022]

Ans. 20
l = 300 cm
ε = Kx
20 × 10⁻³ =
R = 20

Q.37. Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length l₁ is 40 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the value of x will be ____________ Ω. 
[JEE Main 2022]

Ans. 20

24 = 4 + x
x = 20

Q.38. In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ___________ cm. 
[JEE Main 2022]

Ans. 18
E ∝ I
1.2 / 1.8 = 36 / I′
I′ = 3 / 2 × 36 = 54 cm
ΔI = I′ − I = 54 - 36 = 18 cm

Q.39. Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length 2l have the same resistance (R) then its diameter will be ____________ d. [JEE Main 2022]

Ans. 4
RAB = RR = 1 / 8 (Resistance of one wire)
=
Resistance of copper wire of length 2l and diameter x = R

16d² = x²
x = 4d

Q.40. In the given figure, the value of V_o will be _____________ V. [JEE Main 2022]

Ans. 4
Using Kirchhoff's junction rule.

2 − 3V₀ = 0
V₀  = 4 V

Q.41. The circuit diagram of potentiometer used to measure the internal resistance of a cell (E) is shown in figure. The key 'K' is kept closed so as to send constant current through potentiometer wire. When key 'K1' is kept open the null point is found to be at 120 cm on the potentiometer wire. When the key 'K1' is closed the null point is shifted at 80 cm at the potentiometer wire. The internal resistance of the given cell is _____________ Ω.
[JEE Main 2022]

Ans. 2

Q.42. In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is 3 : 2, the difference in the balancing length of the potentiometer wire in above two cases will be ___________ cm. [JEE Main 2022]

Ans. 25
At balancing point, we know that emf is proportional to the balancing length. i.e., emf ∝ balancing length
Now, let the emf's be 3ε and 2ε.
⇒ 3ε = k(75) ..... (1)
and 2ε = k(l) ....... (2)
⇒ l = 50 cm
⇒ Difference is (75 − 50) cm = 25 cm.

Q.43. A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 25 V battery and an external resistance 30 Ω. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is x10. The value of x is __________.
[JEE Main 2022]

Ans. 25
∴
= 1/2 x 5 = 2.5 volts
= 25 / 10 volts

Q.44. The total current supplied to the circuit as shown in figure by the 5 V battery is ____________ A. [JEE Main 2022]

Ans. 2
⇒ I = 5 / 2.5 = 2 A

Q.45. A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is ____________ J.
[JEE Main 2022]

Ans. 450
300 = I2R × 15
⇒ R = 5Ω
Now I₂²Rt₂
= 9 × 5×10
= 450J

Q.46. The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %. [JEE Main 2022]

Ans. 300
Volume is constant so on length doubled
Area is halved so

So percentage increase will be

= 300%

Q.47. Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10−5 N, then separation between the wires is ____________ cm. 
[JEE Main 2022]

Ans. 5

= 50 mm
= 5 cm

Q.48. The current density in a cylindrical wire of radius 4 mm is 4 × 10⁶ Am⁻². The current through the outer portion of the wire between radial distances R/2 and R is ____________ π A.
[JEE Main 2022]

Ans. 48
i =  A x j

= 48π

Q.49. A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 Ω resistance. The value of internal resistance of the cell will be ____________ Ω. [JEE Main 2022]

Ans. 8

⇒ r₁ = 8Ω

Q.50. In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be √x/2. The value of x is __________. [JEE Main 2022]

Ans. 3

This will be minimum when

so x = 3

Q.51. The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 × 10⁶ A/m². The current through the outer portion of the wire between radial distances r/2 and r is xπ A; where x is __________. [JEE Main 2022]

Ans. 12
i = A x j

= 12π

Q.52. Current measured by the ammeter (A) in the reported circuit when no current flows through 10 Ω resistance, will be ________________ A. [JEE Main 2022]

Ans. 10
For I₁₀ = 0
R₃ = 46
⇒ R = 2Ω
⇒
=
= 10 A

Q.53. A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 Ω. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ____________ Ω. [JEE Main 2022]

Ans. 19

Q.54. All resistances in figure are 1 Ω each. The value of current 'I' is a/5 A. The value of a is _________. [JEE Main 2022]

Ans. 8
Let the current is i
Using Kirchhoff's law

So, a = 8

Q.55. Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resistor, the reading of the voltmeter will be ___________ V. [JEE Main 2022]

Ans. 8
Now
⇒ Reading of voltmeter =400 / 1000×20 = 8 volts

Q.56. For the network shown below, the value of V_B − V_A is ____________ V. [JEE Main 2022]

Ans. 10
V_B − V_A = i × 2
= 15 / 1 + 2 × 2
⇒ V_B − V_A = 10 volts

Q.57. The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x × 10⁻³ Ω cm. The value of x is ____________. 
[Take π = 3.14] [JEE Main 2022]

Ans. 144
Resistance = tan 45^o = 1Ω

⇒ x = 144

Q.58. In Circuit-1 and Circuit- 2 shown in the figures, R₁=1Ω,R₂=2Ω and R₃=3Ω. P₁ and P₂ are the power dissipations in Circuit-1 and Circuit-2 when the switches S₁ and S₂ are in open conditions, respectively. Q₁ and Q₂ are the power dissipations in Circuit-1 and Circuit-2 when the switches S₁ and S₂ are in closed conditions, respectively. (More than One Correct Answer) [JEE Advance 2022]

Which of the following statement(s) is(are) correct?
(a) When a voltage source of 6V is connected across A and B in both circuits, P₁ < P₂.
(b) When a constant current source of 2Amp is connected across A and B in both circuits, P₁ > P₂.
(c) When a voltage source of 6V is connected across A and B in Circuit-1, Q₁ > P₁.
(d) When a constant current source of 2Amp is connected across A and B in both circuits, Q₂ < Q₁.

Ans. a, b, c

Q.59. The figure shows a circuit having eight resistances of 1Ω each, labelled R₁ to R₈, and two ideal batteries with voltages ε₁=12 V and ε₂=6 V. (More than One Correct Answer) 
[JEE Advance 2022]
Which of the following statement(s) is(are) correct?
(a) The magnitude of current flowing through R₁ is 7.2 A.
(b) The magnitude of current flowing through R₂ is 1.2 A.
(c) The magnitude of current flowing through R₃ is 4.8 A.
(d) The magnitude of current flowing through R₅ is 2.4 A.

Ans. a, b, c, d

Q.60. A medium having dielectric constant K>1 fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is d. The capacitor is connected to a battery of voltage V, as shown in Figure (a). Now, both the plates are moved by a distance of d/2 from their original positions, as shown in Figure (b).
[JEE Advance 2022]
In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?
(a) The electric field inside the dielectric material is reduced by a factor of 2K.
(b) The capacitance is decreased by a factor of 1 / K+1.
(c) The voltage between the capacitor plates is increased by a factor of (K+1).
(d) The work done in the process DOES NOT depend on the presence of the dielectric material.

Ans. b

Q.61. Two resistances R₁ = XΩ and R₂ = 1Ω are connected to a wire AB of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from 0.2 mm at A to 1 mm at B. A galvanometer (G) connected to the center of the wire, 50 cm from each end along its axis, shows zero deflection when A and B are connected to a battery. The value of X is ____________. 
[JEE Advance 2022]

Ans. 5

Q.62. In the following circuit C₁ = 12μF, C₂ = C₃ = 4μF and C₄ = C₅ = 2μF. The charge stored in C₃ is ____________ μC.  [JEE Advance 2022]

Ans. 8
From circuit given, Potential difference across C₃ is 2 V (constant)
∴ Q₃ = 2 × 4 μC
= 8μC

Q.63. A uniform heating wire of resistance 36Ω is connected across a potential difference of 240 V. The wire is then cut into half and potential difference of 240V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : x, where x is ____________ [JEE Main 2021]

Ans. 4
For Case I,
The potential difference of the uniform wire, V = 240 V
The resistance of the uniform wire, R₁ = 36 Ω
The power dissipation in the first case, 

For Case II,
The resistance of each half,

Thus, the ratio of the total power dissipation in the first case to the second case

Comparing with, P₁ / P₂ = 1/x
The value of the x = 4.

Q.64. A resistor dissipates 192 J of energy in 1s when a current of 4A is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5s in ______ J.
[JEE Main 2021]

Ans. 3840
E = i²Rt
192 = 16 (R) (1)
R = 12Ω
E1 = (8)² (12) (5)
= 3840 J

Q.65. The voltage drop across 15Ω resistance in the given figure will be ______________ V.
[JEE Main 2021]

Ans. 6
Point drop across 6Ω = 1 × 6 = 6 = V_AB
⇒ Hence point drop across 15Ω = 6 volt = V_AB

Q. 66. A square shaped wire with resistance of each side 3Ω is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of Ω will be_____. 
[JEE Main 2021]

Ans. 3
R_eq = 3

Q.67. The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x : 8. The value of x is ___________. [JEE Main 2021]

Ans. 9

∴ x = 9

Q.68. First, a set of n equal resistors of 10 Ω each are connected in series to a battery of emf 20V and internal resistance 10Ω. A current I is observed to flow. Then, the n resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of n is ............... . [JEE Main 2021]

Ans. 20
In series
R_eq = nR = 10n

In parallel

n = 20

Q.69. For the circuit shown, the value of current at time t = 3.2 s will be _________ A.
[JEE Main 2021]
[Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)] 
[JEE Main 2021]

Ans. 1
From graph voltage at t = 3.2 sec is 6 volt.
i = 6 − 5 / 1
⇒ i = 1 A

Q.70. An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the bulb delivers the same power is _____________ Ω. [JEE Main 2021]

Ans. 50
Power,

R_B = 50Ω
To produce same power, same voltage (i.e. 100 V) should be across the bulb.
Hence, R = R_B
R = 50 Ω

Q.71. In an electric circuit, a cell of certain emf provides a potential difference of 1.25 V across a load resistance of 5Ω. However, it provides a potential difference of 1 V across a load resistance of 2Ω. The emf of the cell is given by x/10V. Then the value of x is ______________. [JEE Main 2021]

Ans. 15
In case (a) ε = 1.25 / 5 (5 + r)
⇒ 4ε = 5 + r ..... (1)
In case (b), ε = 1/2(2 + r)
⇒ 2ε = 2 + r ..... (2)
From equation (1) & (2)
2ε = 3 ⇒ ε = 1.5
or x = 15

Q.72. In the given figure switches S₁ and S₂ are in open condition. The resistance across ab when the switches S₁ and S₂ are closed is _____________ Ω. [JEE Main 2021]

Ans. 10
When switch S₁ and S₂ are closed

= 10Ω

Q.73. Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection. 
[JEE Main 2021]
The value of x, to the nearest integer, is ___________.

Ans. 48
As galvanometer shows zero deflection so it act's as balanced wheatstone bridge.

⇒ 14 − 2x = x
⇒ 3x = 144
⇒ x = 48 cm

Q.74. Two wires of same length and thickness having specific resistances 6Ω cm and 3Ω cm respectively are connected in parallel. The effective resistivity is ρΩ cm. The value of ρ, to the nearest integer, is ____________. [JEE Main 2021]

Ans. 4
Let length of each wire is l and area A. When they are connected in parallel then their effective area 2A.
From formula we know,

Q.75. The voltage across the 10Ω resistor in the given circuit is x volt. [JEE Main 2021]

The value of 'x' to the nearest integer is _________.

Ans. 70



I = 7A
Potential Across 10Ω resister
V₁₀ = IR = 7 × 10 = 70V
⇒ V₁₀ = 70V

Q.76. The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is ____________. (Round off to the Nearest Integer) [JEE Main 2021]

Ans. 4

For real roots, b² - 4ac ≥ 0

⇒ 2 − n ≥±2
⇒ 2 − n ≥ −2
⇒ n ≥ 4
So, minimum value for n = 4

Q.77. The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it. The resistance is ___________Ω. (Round off to the Nearest Integer) 
[JEE Main 2021]

Ans. 2500
Given, energy dissipated by a resistor, H = 10 mJ = 10 × 10−3 J
Time, t = 1 s
Electric current, I = 2 mA = 2 × 10−3 A
Resistance, R = ?
According to Joule's law of heating,
H = I²Rt

Substituting the given values in Eq. (i), we get

⇒ R = 2500Ω

Q.78. In the figure given, the electric current flowing through the 5 kΩ resistor is 'x' mA.
[JEE Main 2021]
The value of x to the nearest integer is ____________.

Ans. 3

∴ I = 3 mA

Q.79. In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The workdone by the battery is __________J. [JEE Main 2021]

Ans. 300
Given, charge passing through circuit, q = 20 C
Potential difference between two plates,
V = 15 V
Let W be the amount of work done by battery.
∴ W = qV = 20 × 15 = 300 J

Q.80. A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2Ω each and leaves by the corner R. The currents i₁ in ampere is _________.
[JEE Main 2021]

Ans. 2
The Current

=
i₁=2A

Q.81. In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E₁ and E₂ as well. For key K₁ (closed), the jockey is adjusted to touch the wire at point J₁ so that there is no deflection in the galvanometer. Now the first battery (E₁) is replaced by second battery (E₂) for working by making K₁ open and K₂ closed. The galvanometer gives then null deflection at J₂. The value of E₁ / E₂ is a/b, where a = _________.[JEE Main 2021]

Ans. 1
Length of AB = 10 m
For battery E₁, balancing length is l₁
l₁ = 380 cm [from end A]
For battery E₂, balancing length is l₂
l₂ = 760 cm [from end A]
Now, we know that
⇒
∴ a = 1 & b = 2
∴ a = 1

Q.82. A cylindrical wire of radius 0.5 mm and conductivity 5 × 10⁷ S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x³π mA. The value of x is _________. [JEE Main 2021]

Ans. 5
We know that current density,
J = σE
⇒ J = 5 × 10⁷ × 10 × 10⁻³
⇒ J = 50 × 10⁴ A/m²
Current flowing;
I = J × πR²
I = 50 × 10⁴ × π(0.5 × 10⁻³)²
I = 5 × 10⁴ × π × 0.25 × 10⁻⁶
I = 125 × 10⁻³π
∴ x = 5 

Q.83. Due to cold weather a 1 m water pipe of cross-sectional area 1 cm² is filled with ice at −10^∘C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 kΩ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3.33 × 10⁵ J kg⁻¹, specific heat of ice = 2 × 10³ J kg⁻¹ and density of ice = 10³ kg/m³  [JEE Main 2021]
(a) 0.353 s
(b) 35.3 s
(c) 3.53 s
(d) 70.6 s

Ans. b
Given, the length of the water pipe, L = 1 m
The cross-sectional area of the water pipe, A = 1 cm² = 10⁻⁴ m²
The temperature of the ice = − 10∘C
Current passing in the conductor, I = 0.5 A
Resistance of the conductor, R = 4 kΩ
The latent heat of fusion for ice, L_f = 3.33 × 10⁵ J/kg
The density of the ice, d = 1000 kg/m³
The specific heat of the ice, c_{p, ice} = 2 × 10³ J/kg
Heat required to melt the ice at 10∘C to 0∘C
Q = mc_pΔT + mL_f ⇒ Q = dVc_pΔT + dVL_f
= 1000 × 10⁻⁴ × 2 × 10³ × (10) + 1000 × 10⁻⁴ × 3.33 × 10⁵ (∵ V = A × L)
= 35300 J
According to the Joule's law of heating,
H = I²Rt
⇒ 35300 = (0.5)²(4000) (t)
⇒ t = 35.3 s
Thus, the minimum time required to melt the ice is 35.3 s. 

Q.84. The equivalent resistance of the given circuit between the terminals A and B is :
[JEE Main 2021]
(a) 0Ω
(b) 3Ω
(c) 92Ω
(d) 1Ω

Ans. d
On simplification

Q.85. Consider a galvanometer shunted with 5Ω resistance and 2% of current passes through it. What is the resistance of the given galvanometer? [JEE Main 2021]
(a) 300 Ω
(b) 344 Ω
(c) 245 Ω
(d) 226 Ω

Ans. c
0.02i Rg = 0.98i × 5
Rg = 245 Ω
Option (c)

Q.86. For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be :
[JEE Main 2021]
(a) 1Ω
(b) 5Ω
(c) 4Ω
(d) 2Ω

Ans. d

Q.87. The Colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is : [JEE Main 2021]
(a) (5700 ± 285) Ω
(b) (7500 ± 750) Ω
(c) (5700 ± 375) Ω
(d) (7500 ± 375) Ω

Ans. d
R = 75 × 102 ± 5% of 7500
R = (7500 ± 375) Ω

Q88. Five identical cells each of internal resistance 1Ω and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same? [JEE Main 2021]
(a) 1 Ω
(b) 25 Ω
(c) 5 Ω
(d) 10 Ω

Ans. a

4R = R
R = 1Ω

Q.89. An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W. [JEE Main 2021]
(a) 20 Ω
(b) 30 Ω
(c) 5 Ω
(d) 10 Ω

Ans. a
500 watt at 100 v
P = Vi
500 = Vi
i = 5 Amp
V = i × R
R = 20

Q.90. If you are provided a set of resistances 2Ω, 4Ω, 6Ω and 8Ω. Connect these resistances so as to obtain an equivalent resistance of 46/3Ω. [JEE Main 2021]
(a) 4Ω and 6Ω are in parallel with 2Ω and 8Ω in series
(b) 6Ω and 8Ω are in parallel with 2Ω and 4Ω in series
(c) 2Ω and 6Ω are in parallel with 4Ω and 8Ω in series
(d) 2Ω and 4Ω are in parallel with 6Ω and 8Ω in series

Ans. d

Q.91. What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3Ω ? [JEE Main 2021]
(Given resistivities of iron and copper-nickel alloy wire are 12 μΩ and 51 μΩ cm respectively)
(a) 82 m
(b) 97 m
(c) 110 m
(d) 90 m

Ans. b

⇒ l = 97 m

Q.92. In the given figure, the emf of the cell is 2.2 V and if internal resistance is 0.6Ω. Calculate the power dissipated in the whole circuit : [JEE Main 2021]
(a) 1.32 W
(b) 0.65 W
(c) 2.2 W
(d) 4.4 W

Ans. c

Q.93. The resistance of a conductor at 15^∘C is 16Ω and at 100∘C is 20Ω. What will be the temperature coefficient of resistance of the conductor? [JEE Main 2021]
(a) 0.010^∘C⁻¹
(b) 0.033^∘C⁻¹
(c) 0.003^∘C⁻¹
(d) 0.042^∘C⁻¹

Ans. c
16 = R₀ [1 + α (15 − T₀)]
20 = R₀ [1 + α (100 − T₀)]
Assuming T₀ = 0∘C, as a general convention. 
⇒
⇒ α = 0.003^∘C⁻¹

Q.94. A simple pendulum of mass 'm', length 'l' and charge '+ q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be [JEE Main 2021]
(a)
(b)
(c)
(d)

Ans. c
Let E be electric field in air
T sinθ = qE
T cosθ = mg


Now,

Q.95. In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii r₁ and r₂ (r₂ < r₁). [JEE Main 2021]
Choose the correct option as one moves from P to Q :(a) Drift velocity of electron increases.
(b) Electric field decreases.
(c) Electron current decreases.
(d) All of these

Ans. a
Current is constant in conductor
i = constant
Resistance of element

if r decreases, E will increase : V_d will increase

Q.96. The given potentiometer has its wire of resistance 10Ω. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2Ω resistor is :
[JEE Main 2021]
(a) 10 V
(b) 5 V
(c) 40/9 V
(d) 40/11 V

Ans. c

Potential difference across 2Ω resistor is 20 − V₀
That is (20 − 140 /9) Volt
Hence answer is (40/9) Volt

Q.97. In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells, ε₁/ε₂ is : [JEE Main 2021]
(a) 5/3
(b) 8/5
(c) 4/3
(d)  3/2

Ans. a

Q.98. In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 Ω per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is :
[JEE Main 2021]

(a) 5 V
(b) 2.25 V
(c) 6 V
(d) 2.75 V

Ans. a
Max. voltage that can be measured by this potentiometer will be equal to potential drop across AB
RAB = 10 × 0.1 × 100 = 100 ohm.

Q.99. A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take Resistivity of Copper = 1.7 × 10⁻⁸ Ωm and Resistivity of Aluminium = 2.6 × 10⁻⁸ Ωm) 
[JEE Main 2021]

(a) 0.0858 mΩ
(b) 1.420 mΩ
(c) 0.858 mΩ
(d) 2.170 mΩ

Ans. c

= 0.856 mΩ

Q.100. The value of current in the 6 Ω resistance is : [JEE Main 2021]
(a) 4A
(b) 8A
(c) 10A
(d) 6A

Ans. c
The given figure can be represented as
From the above figure, it can be clearly seen that the voltage across point R is assumed as V.
Therefore, applying Kirchhoff's current law at point R, we can write

⇒ 25V = 1500 ⇒ V = 60V
Therefore, current through 6Ω resistor is

Q.101. In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is : [JEE Main 2021]
(a) 3.9
(b) 8.4
(c) 7.5
(d) 3.0

Ans. a

Q.102. The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC. [JEE Main 2021]
(a) 4.87 μA
(b) 4.87 mA
(c) 2.44 mA
(d) 2.44 μA

Ans. b

Similarly,

after solving equation (1) & (2)
V_D = 0.79 volt
V_B = 0.86 volt
Then the current through the galvanometer

Q.103. Two cells of emf 2E and E with internal resistance r₁ and r₂ respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is [JEE Main 2021]

(a) r₁ − r₂
(b) r₁/2 − r₂
(c) r₁/2 + r₂
(d) r₁ + r₂

Ans. b

V_A = V_B
2E = ir₁

Q.104. A current of 10A exists in a wire of cross-sectional area of 5 mm² with a drift velocity of 2 × 10⁻³ ms⁻¹. The number of free electrons in each cubic meter of the wire is ___________.
[JEE Main 2021]
(a) 625 × 10²⁵
(b) 1 × 10²³
(c) 2 × 10²⁵
(d) 2 × 10⁶

Ans. a

Q.105. A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in 20 s. [JEE Main 2021]
(a) 1000 J
(b) 2000 J
(c) 1500 J
(d) 500 J

Ans. b

Q.106. A conducting wire of length 'l', area of cross-section A and electric resistivity ρ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.
If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be : [JEE Main 2021]

(a)
(b)
(c)
(d)

Ans. c
We know that

Now, new length : l′ = 2l
new area of cross section : A′ = A/2
∴ New resistance :  

∴ Resultant current :  I = V / 4R
⇒

Q.107. A wire of 1Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is : [JEE Main 2021]
(a) 76%
(b) 12.5%
(c) 25%
(d) 56%

Ans. d
R₀ = 1
R₁ = ?
l₀ = 1m
l₁ = 1.25 m
A₀ = A
As volume of wire remains constant so

Now
Resistance (R) = pl / A

So % change in resistance

= 56.25%

Q.108. Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is : [JEE Main 2021]
(a) 3R/2
(b) R/2
(c) 2R
(d) R

Ans. d
Given all resistances have same resistance R.
Now, we can redraw the circuit as below
Let resistances be R₁, R₂, R₃ and R₄. 

So, circuit will behave as a Wheatstone bridge and no current will flow through middle resistor.
∴
=
= R

Q.109. A cell E₁ of emf 6V and internal resistance 2Ω is connected with another cell E₂ of emf 4V and internal resistance 8Ω (as shown in the figure). The potential difference across points X and Y is : 
[JEE Main 2021]
(a) 10.0 V
(b) 2.0 V
(c) 5.6 V
(d) 3.6 V

Ans. c
The circuit can be shown as below
The current through the circuit,

∴ Potential difference across points X and Y is
V_XY = E₂ + Ir₂ = 4 + 15 × 8 = 5.6V

Q.110. A current through a wire depends on time as
i = α₀t + βt² where α₀ = 20 A/s and β = 8 As⁻². Find the charge crossed through a section of the wire in 15s. [JEE Main 2021]
(a) 2250 C
(b) 2100 C
(c) 260 C
(d) 11250 C

Ans. d
Given, i = α₀t+βt²
where, α₀ = 20 A/s, β = 8 A/s²
We know that, i = dq / dt
⇒
⇒ dq = (20t + 8t²)dt
On integrating both sides, we get


∴ q = 11250 C