advertisement

**8**

**Q Calculate the total (eff ective) capacitance for each of the three circuit arrangements shown in (a), (b), and (c) below.**

C 2 C 1 C 2 50 pF 25 pF C 1 5 µ F C 2 10 µ F C 1 2 µ F C 3 C 4 5 µ F C 5 0.4 µ F C 6 6.6 µ F 8 µ 2 µ F F (a) (b)

**A (a) (b)**

*C C*

1 50 50 1 6 67 2

*C*

2 picofarad 25 25

*C C*

1

*C*

2 microfarad 1 0 (c)

**(c)**

A labelled circuit diagram is shown below.

C 2 5 µ F C 5 8 µ F A C 1 2 µ F B C 3 0.4 µ F C C 6 2 µ F D C 4 6.6 µ F

*C CD C BC*

1

*C C*

5

*C*

2 1 2 µ

*C*

6 microfarad

*C*

3

*C*

4 microfarad 1 1 1

*C AB C BC*

30 1 .

60 46 µ

**Ans**

*C*

4

*CD*

1 6 0 1 1 1 2 1 0 µ F 1 1 0

**Q A capacitor network connected to a d.c. supply is shown below. Calculate (a) the charge drawn from the supply, (b) the charge on C 3 , and (c) the p.d. across C 1 .**

C 1 4 µ F C 3 8 µ F B C C 2 6 µ F A

**9**

V 120 V

**A (a)**

*C AB C*

1 1 0

*C*

2 microfarad 6

*AB C AC C AC C*

.

*AB*

µ 3

*C*

3 microf 1 1 0 0 8 8 so

*Q Q VC AC*

coulomb 533 µ

**Ans**

1 20 1 0 6

**(b)**

The equivalent circuit is shown below, in which each of the two eff ective capacitors will receive the same value of charge,

*Q*

coulomb, from the supply.

C AB C 3 B A C 10 µ F 8 µ F V AB V BC V 120 V

**10**

Hence the charge on

*C*

3 533 µ C **Ans**

*Q*

**(c)**

From the above fi gure,

*V AB*

volt

*C AB*

so, p.d. across

*C*

1 (and

*C*

2 )

*V AB *

53.3 V **Ans** 533 1 0 1 0 1 0 6 6 This result may be checked by calculating the p.d. across

*C*

3 , thus:

*V BC*

533 8 1 1 0 0 6 6 V

*V AB V BC*

11 which, allowing for rounding error, is 1 20 V.

**Q For the circuit shown below determine (a) the p.d. V 2 , (b) the value of C 2 , and (c) the value of C 3 and the energy stored in C 3 .**

C 1 C 2 C 3 10 µ F 19.35 V V 2 48.38 V

**A (a)**

*V*

2 1 00 ( 1 .

) 1 00

*V*

2

**(b)**

Being a series circuit, all three capacitors will receive the same value of charge from the supply; i.e. the total circuit charge

*Q*

, where

*Q Q*

3

*Q*

2 V 100 V

*Q*

1

*Q*

2

*C*

2 coulomb 1 1 0 1 93 5

*Q V*

2 farad 1 .

1 0 6 1 0 6

**(c)**

3

*W*

3

*W*

3

*C*

3

*C Q*

3

*V*

3 4 µ farad

**Ans**

1 1 2

*C V*

2 joule

**Ans**

6 µ

**Ans**

.

1 0 6 1 0 6 .

2