Answer Essay 18 Capacitor 2005.pdf

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12 (a) State two functions of the dielectric in a capacitor.

[2 marks]

● To reduce the potential difference across the plates  To solve the problem of maintaining two large metal sheets at very small separation.  To increase the storage of charges./ capacitance  Can tolerate stronger electric field without breakdown. [Any two]

[2] 2

(b) Two pure capacitors with capacitance C1 = 5.0 F and C2 = 10.0 F are connected in series to a 10.0 V battery. (i) Derive an expression for the effective capacitance CT of the circuit and calculate the value of CT. [4 marks] C2

C1

10F

5F

10 V Q1  Q2  QT or VT  V1 + V2

[1]

CV  Q

[1]

1 1 1 C 2  C1    CT C1 C 2 C1C 2

or 

CT  

CT 

or

C1C 2 C1  C 2

[1]

(5F)(10 F) (5  10) F

50 F  3.33F 15

[1] 4

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(ii) Calculate the total energy stored in the circuit. Energy stored U 



1 2 C T VT or 2

1 Q2 2 C

or

[2 marks]

1 QV 2

[1]

1 (3.33F)10 2 V 2

 166.5  106 J  1.67  104 J or 1.65 104 J

[1]

1.7

2

(c) The battery in (b) is replaced by an alternating current supply of maximum voltage 10 V and frequency 120 Hz. (i) Calculate the reactance of the combined capacitor.

C1

CT = 3.33 F

C2



V0  10 V

[2 marks]

  Ω

f  120 Hz

Reactance is inversely proportional to the frequency of the alternating current supply. 1 XC  2fC 1  2 (120 Hz) (3.33 F)  398  or 402  or 400 

[1]

[1] 2

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(ii) Calculate the maximum current in the circuit. Comment on the phase of the current with reference to the voltage supplied. [3 marks] The current is I 0  

V0 XC

[1]

10 V 398.3 

 0.025 A

[1]

The current leads the voltage/ voltage lags current by 90° or



[1]

2

3

(iii) Describe briefly the behaviour of the energy stored in the combined capacitor during a cycle of the alternating current supply. [2 marks]

For

In the 1st half of the cycle of the circuit, charges accumulate in capacitor and thus energy is being stored.

[1]

next

Then during the 2nd half cycle the, capacitor is being discharges therefore energy is returned to the voltage source.

[1] 2

For

1st

quarter, capacitor is charged, energy is stored.

(1)

For 2nd quarter, capacitor discharges, energy is returned to the source. (1) or For 3rd quarter, capacitor is charged with the opposite polarity, energy is stored. (1) For 4th quarter, capacitor discharges, energy is returned to the source.

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15

(1)

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