Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

DC Pandey (Questions & Solutions) of Physics: NEET

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NEET : Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

The document Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev is a part of the NEET Course DC Pandey (Questions & Solutions) of Physics: NEET.
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Introductory Exercise 22.1

Ques 1: Find the dimensions of capacitance.
Sol: Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
= [M-1L-2T4A2]

Ques 2: No charge will flow when two conductors having the same charge are connected to each other. Is this statement true or false?
Sol:
Charge does not flow if their potentials are same.

Ques 3: Two metallic plates are kept parallel to one another and charges are given to them as shown in figure. Find the charge on all the four faces.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Sol:
Charge on outermost surfaces
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Hence, charges are as shown below
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 4: Charges 2q and -3g are given to two identical metal plates of area of cross-section A. The distance between the plates is d. Find the capacitance and potential difference between the plates.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Sol: 
Charge on outermost surfaces.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Hence charge on different faces are as shown below.

Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Electric field and hence potential difference between the two plates is due to ±2.5 q
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Introductory Exercise 22.2

Ques 1: Find the charge stored in all the capacitors.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Sol:
All three capacitors are in parallel wit h the battery. PD across each of them is 10V. So, apply q = CV for all of them.

Ques 2: Find the charge stored in the capacitor.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Sol: 
Capacitor and resistor both are in parallel wit h the battery. PD across capacitor is 10V. Now apply q = CV.

Ques 3: Find the charge stored in the capacitor.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Sol: 
In steady state current flows in lower loop of the circuit.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Now, potential difference across capacitor = potential difference across 4Ω resistance.
= iR
= (3)(4)=12V
q = CV = (2μF) (12 V)
= 24μC

Ques 4: A 2μF capacitor and a 2μF capacitor are connected in series across a 1200 V supply line.
(a) Find the charge on each capacitor and the voltage across them.
(b) The charged capacitors are disconnected from the line and from each other and reconnected with terminals of like sign together. Find the final charge on each and the voltage across them.

Sol: 
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
= 800μC
In series, q remains same
q1 = q2 = 800 μC
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
and
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
(b) Now total charge will become 1600 μC. This will now distribute in direct ratio of capacity
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
They will have a common potential (in parallel) given by.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 5: A 100 μF capacitor is charged to 100 V. After the charging, battery is disconnected. The capacitor is then connected in parallel to another capacitor. The final voltage is 20 V. Calculate the capacity of second capacitor.
Sol:
Charge, q = CV = 104μC
In parallel common potential is given by
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
Solving this equation we get
C = 400μF

Introductory Exercise 22.3

Ques 1: An uncharged capacitor C is connected to a battery through a resistance R. Show that by the time the capacitor gets fully charged, the energy dissipated in R is the same as the energy stored in C.
Sol: 
Charge supplied by the battery,
q= CV
Energy supplied by the battery,
E = qV =CV2
Energy stored in the capacitor,
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ Energy dissipated across R in the form of heat = E - U
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 2: How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value?
Sol:

Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 3: A capacitor of capacitance C is given a charge q0. At time t = 0 it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the first capacitor and the second capacitor as a function of time f. Also plot the corresponding q-t graphs.
Sol:
Both capacitors have equal capacitance. Hence half-half charge distribute over both the capacitors.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
q1 decreases exponentially from Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
While q2 increases exponentially from Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev Corresponding graphs and equation are given in the answer. Time constant of two exponential equations will be
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 4: A capacitor of capacitance C is given a charge q0. At time f = 0, it is connected to a battery of emf E through a resistance R. Find the charge on the capacitor at time t.
Sol: qi = q0 qf = EC
Now charge on capacitor changes from qto qf exponentially.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 5: Determine the current through the battery in the circuit shown in figure
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

(a) immediately after the switch S is closed
(b) after a long time.
Sol: (a) Immediately after the switch is closed whole current passes through C
i = E/R1
(b) Long after switch is closed no current will pass through C1 and C2.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 6: For the circuit shown in figure find
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
(a) the initial current through each resistor
(b) steady state current through each resistor
(c) final energy stored in the capacitor
(d) time constant of the circuit when switch is opened.
Sol: 
(a) At t = 0 equivalent resistance of capacitor is zero. R1 and R2 are in parallel across the battery PD across each is E.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
(b) In steady state no current flow through capacitor wire. PD across R1 is E.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
(c) In steady state potential difference across capacitor is E.
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev
(d) When switch is opened, capacitor is discharged through resistors R1 and R2
Capacitors - Physics, Solution by DC Pandey NEET Notes | EduRev

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