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In the circuit shown, if v(t) = 2 sin(1000 t) volts, R = 1 kΩ and C = 1 μF, then the steady-state current i(t), in milliamperes (mA), is
- sin(1000 t) + cos(1000 t)
- 2 sin(1000 t) + 2 cos(1000 t)
- 3 sin(1000 t) + cos(1000 t)
- sin(1000 t) + 3 cos(1000 t)
Correct answer: sin(1000 t) + cos(1000 t)
Solution
The correct option represents the steady-state current in the circuit, which is derived from the voltage across the capacitor and the resistor. The current through the capacitor leads the voltage by 90 degrees, resulting in a sine and cosine combination that reflects the phase shift and the impedance of the circuit.
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