Chapter 3 - Routledge

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Chapter 3

8

Worked Example 1

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

Supplementary Worked Examples

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

Worked Example 2

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

Supplementary Worked Examples

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.

Worked Example 3

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

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