An alternating voltage given by the equation v(t) = 200 (100t) is applied across a pure capacitor of capacitance 50 F . The corresponding time-domain equation for the current i(t) in the circuit is: (Assume v(t) is in volts, i(t) is in amperes, and t is in seconds)

Step-by-step solution

Comparing the given voltage equation v(t) = 200 (100t) with the standard form v(t) = V₀ ( t) , we get: Peak voltage, V₀ = 200 V Angular frequency, = 100 rad/s The capacitive reactance is: X_C = 1 C = 1 100 50 10⁻⁶ = 1 5 10⁻³ = 200 The peak current is: I₀ = V₀ X_C = 200 200 = 1.0 A In a purely capacitive circuit, the current leads the voltage by a phase angle of 2 . Therefore, the equation for the current is: i(t) = I₀ ( t + 2 ) = 1.0 (100t + 2 ) Answer: i(t) = 1.0 (100t + 2 )