A resistor of 100 , inductor of self inductance ( 4 ^2 ) H and a capacitor of unknown capacity are connected in series to an a.c. source of 200 V and 50 Hz. When the current and voltage are in phase, the value of capacity is

Step-by-step solution

When current and voltage are in phase, the circuit is in resonance. X_L = X_C L = 1 C C = 1 ^2 L Given f = 50 Hz, = 2 f = 100 rad/s and L = 4 ^2 H. Substituting the values: C = 1 (100 )^2 ( 4 ^2 ) C = 1 10000 ^2 4 ^2 C = 1 40000 F C = 25 10⁻⁶ F = 25 F Answer: 25 F