NEET Exam  >  NEET Notes  >  Physics Class 12  >  DC Pandey Solutions: Capacitors

DC Pandey Solutions: Capacitors | Physics Class 12 - NEET PDF Download

Introductory Exercise 22.1

Q.1. Find the dimensions of capacitance.

Sol. DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
= [M-1L-2T4A2]

Q.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.

Q.3. Two metallic plates are kept parallel to one another and charges are given to them as shown in the figure. Find the charge on all four faces.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Sol. Charge on outermost surfaces
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
Hence, charges are as shown below
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Q.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.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Sol. Charge on outermost surfaces.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
Hence charge on different faces are as shown below.

DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
Electric field and hence potential difference between the two plates is due to ±2.5 q
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Introductory Exercise 22.2

Q.1. Find the charge stored in all the capacitors.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

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.

Q.2. Find the charge stored in the capacitor.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Sol. Capacitor and resistor both are in parallel with the battery. PD across the capacitor is 10V. Now apply q = CV.

Q.3. Find the charge stored in the capacitor.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

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

Q.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. 
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
= 800μC
In series, q remains same
q1 = q2 = 800 μC
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
and
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
(b) Now total charge will become 1600 μC. This will now distribute in direct ratio of capacity
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
They will have a common potential (in parallel) given by.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Q.5. A 100 μF capacitor is charged to 100 V. After the charging, the battery is disconnected. The capacitor is then connected in parallel to another capacitor. The final voltage is 20 V. Calculate the capacity of the second capacitor.

Sol. Charge, q = CV = 104μC
In parallel common potential is given by
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
Solving this equation we get
C = 400μF

Introductory Exercise 22.3

Q.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,
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
∴ Energy dissipated across R in the form of heat = E - U
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

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

Sol.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Q.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.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
q1 decreases exponentially from DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
While q2 increases exponentially from DC Pandey Solutions: Capacitors | Physics Class 12 - NEET Corresponding graphs and equation are given in the answer. Time constant of two exponential equations will be
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Q.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.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Q.5. Determine the current through the battery in the circuit shown in figure
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

(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.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

Q.6. For the circuit shown in the figure find
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
(a) the initial current through each resistor
(b) steady-state current through each resistor
(c) final energy stored in the capacitor
(d) the time constant of the circuit when the 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.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
(b) In steady state no current flow through capacitor wire. PD across R1 is E.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
(c) In steady state potential difference across capacitor is E.
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET
(d) When switch is opened, capacitor is discharged through resistors R1 and R2
DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

The document DC Pandey Solutions: Capacitors | Physics Class 12 - NEET is a part of the NEET Course Physics Class 12.
All you need of NEET at this link: NEET
105 videos|426 docs|114 tests

Up next

FAQs on DC Pandey Solutions: Capacitors - Physics Class 12 - NEET

1. What is the formula to calculate the capacitance of a capacitor?
Ans. The formula to calculate the capacitance of a capacitor is C = Q/V, where C is the capacitance in Farads, Q is the charge stored on the capacitor in Coulombs, and V is the voltage across the capacitor in Volts.
2. How does a capacitor store electric charge?
Ans. A capacitor stores electric charge by accumulating opposite charges on its two plates. When a voltage is applied across the capacitor, electrons are attracted to the positive plate and repelled from the negative plate, creating an electric field between the plates. This accumulation of charge on the plates results in the storage of electric energy in the capacitor.
3. What factors affect the capacitance of a capacitor?
Ans. The capacitance of a capacitor is affected by three main factors: the area of the plates, the distance between the plates, and the dielectric constant of the material between the plates. Increasing the plate area or decreasing the plate distance increases the capacitance, while using a material with a higher dielectric constant also increases the capacitance.
4. How does a dielectric affect the capacitance of a capacitor?
Ans. A dielectric material placed between the plates of a capacitor increases the capacitance. This is because the dielectric reduces the electric field between the plates, allowing more charge to be stored for a given voltage. The dielectric constant of the material determines how much the capacitance is increased.
5. What are some common applications of capacitors?
Ans. Capacitors have various applications in electronic circuits. Some common uses of capacitors include smoothing power supply voltages, filtering noise in audio circuits, timing in oscillators, storing and releasing energy in flash cameras, and providing backup power in uninterruptible power supplies (UPS).
105 videos|426 docs|114 tests
Download as PDF

Up next

Explore Courses for NEET exam

How to Prepare for NEET

Read our guide to prepare for NEET which is created by Toppers & the best Teachers
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Summary

,

Extra Questions

,

practice quizzes

,

Sample Paper

,

Viva Questions

,

MCQs

,

pdf

,

Exam

,

DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

,

video lectures

,

Previous Year Questions with Solutions

,

Important questions

,

shortcuts and tricks

,

Free

,

ppt

,

study material

,

Objective type Questions

,

past year papers

,

Semester Notes

,

DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

,

mock tests for examination

,

DC Pandey Solutions: Capacitors | Physics Class 12 - NEET

;