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In the circuit shown in the figure below, for what value of C will the current I be in phase with the sinusoidal source voltage Vs = sin 2t?
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1 F 4 -
1 F 2 -
1 F √2 - 1F
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Correct Option: B
The given circuit: 
Given, Vs = sin 2t, means = 2 rad/sec.
In order to make the current I in phase with the sinusoidal source voltage, the imaginary part of the net impedance offered by the voltage source must be zero.
So,
| Zeq = | || (1 + j1) | |
| j C |
or
| Zeq = | × (1 + j) | |||
| j2C | ||||
| + (1 + j) | ||||
| j2C | ||||
or
| Zeq = | × [1 + j] | |
| 2C | ||
2C – 1 = 0 (Since Imaginary part must be zero)
or
C = 1/2 F
Hence alternative (B) is the correct choice.
