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Q.1. A copper wire of length 10 m and radius (10^{−2}/√π) m has an electrical resistance of 10 Ω. The current density in the wire for an electric field strength of 10 (V/m) is: (2022)
(1) 10^{6} A/m^{2}
(2) 10^{–5} A/m^{2}
(3) 10^{5 }A/m^{2}
(4) 10^{4} A/m^{2}
Answer: (3)
Q.2. A Wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P, and Q (2022)
(1) Should be approximately equal and are small
(2) Should be very large and unequal
(3) Do not play any significant role
(4) Should be approximately equal to 2X
Answer: (1)
We know, a Wheatstone bridge is said to be most precise when it is most sensitive. This can be done by making the ratio arms equal. Thus (1) is correct option.
Q.3. Two resistors of resistance, 100 Ω and 200 Ω are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in 100 Ω to that in 200 Ω in a given time is
(1) 2 : 1
(2) 1 : 4
(3) 4 : 1
(4) 1 : 2 (2022)
Answer (1)
Sol.
Q.4. As the temperature increases, the electrical resistance (2022)
(1) Decreases for both conductors and semiconductors
(2) Increases for conductors but decreases for semiconductors
(3) Decreases for conductors but increases for semiconductors
(4) Increases for both conductors and semiconductors
Answer (2)
Sol. As the temperature increases, the resistivity of the conductor increases hence the electrical resistance increases. However, for semiconductors, the resistivity decreases with the temperature. Hence electrical resistance of semiconductors decreases.
Q.5. Column I gives certain physical terms associated with flow of current through a metallic conductor.
ColumnII gives some mathematical relations involving electrical quantities.
Match ColumnI and ColumnII with appropriate relations. (2021)
A: (A)(R), (B)(P), (C)(S), (D)(Q)
B: (A)(R), (B)(Q), (C)(S), (D)(P)
C: (A)(R), (B)(S), (C)(P), (D)(Q)
D: (A)(R), (B)(S), (C)(Q), (D)(P)
Ans: C
Q.6. In a potentiometer circuit, a cell of EMF 1.5 V gives a balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs? (2021)
A: 64 cm
B: 62 cm
C: 60 cm
D: 21.6 cm
Ans: C
Q.7. The effective resistance of a parallel connection that consists of four wires of equal length,equal area of crosssection and same material is 0.25Ω. What will be the effective resistance if they are connected in series? (2021)
A: 1Ω
B: 4Ω
C: 0.25Ω
D: 0.5Ω
Ans: B
R = 1Ω
R_{series} = 4R
= 4(1)
= 4Ω.
Q.8. Three resistors having resistances r_{1}, r_{2} and r_{3} are connected as shown in the given circuit. The ratio i_{3}/i_{1}of currents in terms of resistances used in the circuit is: (2021)
A:
B:
C:
D:
Ans: D
v = ir
i = v/r
i ∝ i/r
[ v is same for r_{2 }& r_{3}]
Q.9. Which of the following graph represents the variation of resistivity (r) with temperature (T) For copper? (2020)
A:
B:
C:
D:
Ans: A
Relation between resistivity and temperature is given by ρ = ρ_{0}e^{αT}
Q.10. A charged particle having drift velocity of 7.5×10^{4} m s^{1} in an electric field of 3×10^{10} Vm^{1} has a mobility in m^{2} V^{1} s^{1} of : (2020)
A: 2.5×10^{6}
B: 2.25×10^{15}
C: 2.25×10^{15}
D: 2.5×10^{6}
Ans: D
μ = 2.5 × 10^{6}
(μ = mobility)
Q.11. The color code of a resistance is given below:
The values of resistance and tolerance, respectively, are : (2020)
A: 4.7 kΩ, 5%
B: 470Ω, 5%
C: 470 kΩ, 5%
D: 47 kΩ, 10%
Ans: B
R = 47 × 10^{1}Ω ± 5%
= 470 Ω ± 5%
So, 470, 5%
Q.12. The solids which have the negative temperature coefficient of resistance are : (2020)
A: semiconductors only
B: insulators and semiconductors
C: metals
D: insulators only
Ans: B
Insulators have a negative temperature coefficient because as temperature increases, the resistance of insulators decreases. The resistivity of the semiconductor material to decrease with the rise in temperature, resulting in a negative temperature coefficient of resistance.
Q.13. Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance. (2019)
The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be : (2019)
A: 4 : 9
B: 9 : 4
C: 1 : 2
D: 2 : 1
Ans: B
Solution:
(i) All bulbs are glowing
(ii) Two from section A and one from section B are glowing.
Q.14. In the circuits shown below, the readings of the voltmeters and the ammeters will be (2019)
A: V_{2} > V_{1} and i_{1} = i_{2}
B: V_{1} = V_{2} and i_{1} > i_{2}
C: V_{1} = V_{2} and i_{1} = i_{2}
D: V_{2} > V_{1} and i_{1} > i_{2}
Ans: C
Solution:
For ideal voltmeter, resistance is infinite and for the ideal ammeter, resistance is zero.
Q.15. A set of 'n' equal resistors, of value 'R' each, are connected in series to a battery of emf 'E' and internal resistance 'R'. The current drawn is I. Now,the 'n' resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10 I. The value of 'n' is : (2018)
A: 10
B: 11
C: 20
D: 9
Ans: A
Solution:
Q.16. A battery consists of a variable number 'n' of identical cells (having internal resistance 'r' each) which are connected in series. The terminals of the battery are shortcircuited and the current I is measured. Which of the graphs shows the correct relationship between I and n ? (2018)
A:
B:
C:
D:
Ans: A
Solution:
Q.17. Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is (2018)
A: 40 Ω
B: 25 Ω
C: 250 Ω
D: 500 Ω
Ans: C
Solution:
Q.18. The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be : (2017)
A: R/n
B: n^{2}R
C: R/n^{2}
D: nR
Ans: B
Solution:
Q.19. A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves : (2017)
A: Potential gradients
B: A condition of no current flow through the galvanometer
C: A combination of cells, galvanometer and resistances
D: Cells
Ans: B
Solution:
In zero deflection condition, potentiometer draws no current.
Q.20. A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emf's is : (2016)
A: 3:2
B: 5:1
C: 5:4
D: 3:4
Ans: A
Solution: According to question, emf of the cell is directly proportional to the balancing length.
i.e., E∝ ℓ ... (i)
Now, in the first case, cells are connected in series
That is,
Net EMF = E_{1} + E_{2}
From equation (i),
E_{1} + E_{2} = 50 cm (given) ... (ii)
Now, the cells are connected in series in the opposite direction,
Net emf = E_{1}  E_{2}
From equation (i)
E_{1}  E_{2} = 10 ... (iii)
From equation (ii) and (iii),
Q.21. The charge flowing through a resistance R varies with time t as Q = at  bt^{2}, where a and b are positive constants. The total heat produced in R is : (2016)
A: a^{3}R/b
B: a^{3}R/6b
C: a^{3}R/3b
D: a^{3}R/2b
Ans: B
Solution:
Given,
Charge, Q = at  bt^{2} ... (i)
We know that,
Current, I = dθ/dt
So, equation (i) can be written as,
For maximum value of t, the current is given by,
a2bt = 0
Therefore, t = a/2b ..(iii)
Total heat produced (H) can be given as,
On solving the above equation, we get
Given,
Charge, Q = at  bt^{2} ... (i)
We know that,
Current, I = dθ/dt
So, equation (i) can be written as,
For maximum value of t, the current is given by,
a2bt = 0
Total heat produced (H) can be given as,
On solving the above equation, we get
Q.22. A, B and C are voltmeters of resistance R, 1.5 R and 3R respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are VA, VB and VC respectively. (2015)
Then :
A:
B:
C:
D:
Ans: B
Solution:
Q.23. A potentiometer wire has length 4 m and resistance 8 Ω. The resistance that must be connected in series with the wire and an accumulator of e.m.f. 2V, so as to get a potential gradient 1 mV per cm on the wire is : (2015)
A: 48 Ω
B: 32 Ω
C: 40 Ω
D: 44 Ω
Ans: B
Solution:
Figure alongside shows a potentiometer wire of length L = 4m and resistance RAB = 8Ω. Resistance connected in series is R.
When an accumulator of emf ε = 2V is used, we have current I given by,
The resistance per unit length of the potentiometer wire is given by,
Q.24. Across a metallic conductor of nonuniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is : (2015)
A: electric filed
B: current density
C: current
D: drift velocity
Ans: C
Solution:
As the crosssectional area of the conductor is nonuniform so current density will be different.
As, I = JA
It is clear from Eq. (i) when an area increases the current density decreases so the number of the flow of electrons will be same and thus the current will be constant.
Q.25. In an ammeter 0.2% of main current passes through the galvanometer. If resistance of galvanometer is G, the resistance of ammeter will be: (2014)
A: 1/500 G
B: 500/499 G
C: 1/499 G
D: 499/500 G
Ans: A
Solution:
Let the shunt resistance be S.
Q.26. The resistance in the two arms of the meter bridge are 5 Ω and R Ω, respectively. When the resistance R is shunted with an equal resistance, the new balance point is at 1.6ℓ_{1}. The resistance ‘R’ is : (2014)
A: 20 Ω
B: 25 Ω
C: 10 Ω
D: 15 Ω
Ans: B
Solution:
Q.27. Two cities are 150 km apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is 8 volt and the average resistance per km is 0.5 Ω. The power loss in the wire is : (2014)
A: 19.2 J
B: 12.2 kW
C: 19.2 W
D: 19.2 kW
Ans: D
Solution:
Total voltage drop across wire = 150 x 8
= 1200 volt
Total resistance of wire
= 150 x 0.5 = 75 Ω
∴ current through wire
Q.28. A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of 2.0 V and a negligible internal resistance. The potentiometer wire itself is 4 m long. When the resistance, R connected across the given cell, has value of.
(i) infinity
(ii) 9.5 Ω, the ‘balancing lengths’ , on the potentiometer wire are found to be 3m and 2.85m,respectively.
The value of internal resistance of the cell is: (2014)
A: 0.5 Ω
B: 0.75 Ω
C: 0.25 Ω
D: 0.95 Ω
Ans: A
Solution:
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