# Numerical Problems : Capacitor

##### LEVEL – I

Q: 1. Find the equivalent capacitance between the ends P and Q. The plates are of area A, and the distance between them is d. The dielectric constants are k1 and k2 where k1 = 2 and k2 = 4 of material.

Ans: $latex \displaystyle (\frac{\sqrt{208}-8}{6})C \; C = \frac{\epsilon_0 A}{d}$

Q: 2. The plates of a parallel plate capacitor, having area ‘ A ‘, are maintained at constant potential difference ‘ V ‘ . If the initial separation between the plates is ‘ d ‘ , find the work done in increasing the separation of plates to ‘ 2d ‘ .

Ans: $latex \displaystyle \frac{1}{4} \frac{\epsilon_0 A}{d} V^2$

Q: 3. A 1 μF and a 2μF capacitor are connected in series across a 1200 V supply.
(a) Find the charge on each capacitor and the voltage across each capacitor.
(b) The charged capacitors are disconnected from the line and from each other, and are now reconnected with terminals of like charge connected together. Find the final charge on each capacitor and the voltage across each capacitor.

Ans: (a) 800 μC , 800 V , 800 μC , 400 V

(b) (1600/3 ) V, (1600/3 ) μC , (3200 /3 ) μC

Q: 4. A capacitor is filled with two dielectrics of the same dimensions but of dielectric constant 2 and 3 respectively. Find the ratio of capacities in the two possible arrangement.

Ans: 24/25

Q:5. A battery of 10 V is connected to a capacitor of capacity 0.1F. The battery is now removed and this capacitor is connected to a second uncharged capacitor. If the charge is equally distributed on these two capacitors, find the total energy stored in the two capacitors. Find the ratio of final energy to the initial energy.

Ans: 2.5 J . 1/2

Q:6. The distance between the plates of a parallel plate capacitor is 0.05 m. A field of 3 × 104 V/m is established between the plates and an uncharged metal plate of thickness 0.01 m is inserted into the capacitor parallel to its plate. Find potential difference

(a) Before the introduction of the metal plate.

(b) After its introduction.

(c) What would be the potential difference if a plate of dielectric constant K = 2 is introduced in place of metal plate ?

Ans: (a) 1500 Volt (b) 1200 Volt (c) 1350 Volt

Q:7. Two parallel plate capacitors A and B having capacitance 1 μF and 5μF are charged separately to the same potential of 100 volt.

Now the positive plate of A is connected to the negative plate of B and negative plate of A to the positive plate of B.

Find the final charge on each capacitors and total loss of electrical energy in the given system.

Ans: 0.6 × 10-4 C , 3.33 × 10-4 C , (5/3) × 10-2 J

Q:8. Two spherical conductors of radius R and 2R, having potential 4V, and 2V are kept isolated. Find the loss in electrostatic energy if they are connected by a conducting wire.

Ans: $latex \displaystyle \frac{16 \pi \epsilon_0 R V^2}{3}$

Q:9. Find the equivalent capacitance between A and B, if the plates have equal area ‘ A ‘ .

Ans: $latex \displaystyle \frac{2 \epsilon_0 A}{d}[\frac{(k_2 + k_3)k_1}{2k_1 + k_2 + k_3}]$

Q:10. In the given circuit diagram, find the charge which will flow through direction 1 and 2 when the key is closed

Ans: Charge flown through path 2 $latex \displaystyle = – \frac{\epsilon \; C_1 C_2 }{C_1 + C_2}$
Charge flown through path 1 $latex \displaystyle = \epsilon \; C_2$

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