An alternating voltage given by V = 200 2 (100 t) V is applied across a pure capacitor. If the measured RMS current in the circuit is 2 A, the capacitance of the capacitor is:

Step-by-step solution

The given voltage equation is V = 200 2 (100 t) V. Comparing this with the standard equation V = V_m ( t) , we get: Peak voltage, V_m = 200 2 V Angular frequency, = 100 rad/s The RMS voltage is given by: V_ rms = V_m 2 = 200 2 2 = 200 V The RMS current in a purely capacitive circuit is: I_ rms = V_ rms X_C = V_ rms C Substituting the given values ( I_ rms = 2 A): 2 = 200 100 C C = 2 20000 = 10⁻⁴ F Converting to microfarads: C = 10⁻⁴ 10^6 F = 100 F Answer: 100 F