**WORKSHEET # 6 CAPACITANCE**

1.
A Parallel plate capacitor each with plate area A and separation ‘d’ is charged
to a potential difference V. The
battery used to charge it is then disconnected. A dielectric slab of thickness
d and dielectric constant K is now placed between the plates. What change if
any, will take place in

(i) Charge on the plates

(ii) Electric field intensity between the plates,

(iii) Capacitance of the capacitor

Justify your
answer in each case

**.****(Ansi)charge on the capacitor remains unchanged ii) electric field reduces to 1/K times iii)**

**the capacitance increases)**

2. A 2m
insulating slab with a large aluminium sheet of area 1m2 on its top is fixed by a man outside his house one evening.
Will he get an electric shock, if he touches the metal sheet next morning ?

**ANS: Yes**

3.Why the
capacitance of a parallel plate capacitor increases, on introducing a
dielectric medium between the plates?

**ANS:As E decreases, V decreases, therefore C increases)**

4. A
parallel plate capacitor with air between the plates charged. A dielectric is
inserted between the plates. What will happen to its electrostatics potential?
Give reasons.

**ANS: Q = constant ,C increases , V decrease.**

5. The graph
shoes the variation of voltage V across the plates of two capacitors A and B
versus increase of charge Q stored on them. Which of the capacitors has higher capacitance?
Give reason for your answer.

**ANS: V**

_{A}**V**

_{B ,}therefore C_{A}**C**

_{B}
6. How does the energy stored in a capacitor
change if after disconnecting the battery, the plates of a charged capacitor
are moved farther ?

**ANS: Increases**

7. How does
the energy stored in a capacitor change If the plates of a charged capacitor
are moved farther, the battery remaining connected?

**ANS: Decreases**

8. In a parallel plate capacitor with air between the plates, each plate has an area of 6 X 10

^{-3}m2 and the distance between the plates is 3mm. calculate the capacitance of the capacitor. If the capacitor is connected to a 100V supply, what is the charge on each plate of the capacitor?

**ANS: 18pF, 1.8 X 10**

**-**

^{9}

**C**

9. A slab of
material of dielectric constant K has the same area as that of the plates of a
parallel plate capacitor but has the thickness d/2, where d is the separation
between the plates. Find out the expression for its capacitance when the slab
is inserted between the plates of the capacitor.

**ANS:C=2**

_{O}**AK/d(K+1)**

10. A parallel
plate capacitor with air between the plates has a capacitance of 8 PF. The
separation between the plates is now reduced by half and the space between them
is filled with a medium of dielectric constant 5 . Calculate the value of
capacitance of the capacitor in the second case.

**ANS: 80 pF**

11. A very thin plate of metal is placed exactly
in the middle of the two plates of a parallel plate capacitor .What will be the
effect on the capacitance of the system?

**ANS: Capacitance remains unchanged**

12. If C

_{1}=3 pF and C_{2}=2 pF calculate the equivalent capacitance of the given network between points A and B.**ANS: C = 60/61 PF**

13. A
parallel plate capacitor of capacitance C is charged to a potential V .It is
then connected to another capacitor having the same capacitance. Find out the
ratio of the energy stored in the combined system to that stored initially in
the single capacitor?

**ANS: ratio is ½**

14. A technician has only two capacitor. By using
them in series or parallel, he is able to obtain the capacitance of 4, 5, 20,
25 μF .What is the capacitance of both capacitor?

**ANS: 5**

**µ**

**F and 20**

**µ**

**F**

15. Net
capacitance of three identical capacitors in series is 1 μF. What will be their
net capacitance, if connected in parallel? Find the ratio of energy stored in
the two configurations, if they are both connected to the same source ?

**ANS: ratio is 1/9**

16. Three capacitor of
capacitance 2 pF,3pF and 4pF and connected in parallel.

(i) What is the total
capacitance of the combination?

(ii)
Determine the charge on each capacitor, if the combination is connected to a
100V supply

**ANS: i)9PF,ii) 200pc,300pc,400pc**

17. A 4μF
capacitor is charged by a 200V supply. Then, it is disconnected from the supply
and is connected to another uncharged 2μF capacitor. How much electrostatic energy
of the first capacitor is lost in the form of heat and electromagnetic
radiation?

**ANS: 2.67 X 10**

^{-2}

**J**