In the figure, an ac generator with emf E = E m sin ? d t , where E m = 24.9 V a

Question

In the figure, an ac generator with emf E = Em sin ?dt, where Em = 24.9 V and ?d = 382 rad/s, is connected to a 4.38 ?F capacitor. (a) What is the maximum value of the current (in A)? (b) When the current is a maximum, what is the emf (in V) of the generator? (c) When the emf of the generator is - 12.1 V and increasing in magnitude, what is the current (in A)?

In the figure, an ac generator with emf E = Em sin ?dt, where Em = 24.9 V and ?d = 382 rad/s, is connected to a 4.38 ?F capacitor. (a) What is the maximum value of the current (in A)? (b) When the current is a maximum, what is the emf (in V) of the generator? (c) When the emf of the generator is - 12.1 V and increasing in magnitude, what is the current (in A)?

Explanation / Answer

a)

Capacitive reactance X_C = 1 / 2 pi f C = ( 382 rad /s ) (4.30* 10 ^ -6 F ) = 608.79 ohm

b)

Maximum value of current

I = V / Z = 24.9 V /608.79 ohm = 0.04 A

c)

Emf of the generator at maximum current

emf = ( 0.04 A)(608.79 ohm) = 24.9 V

d)

V = emf + I r

I = 24.9 - 12.1 / 608.79 = 0.021 A

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