To light, a 50 W , 100 V lamp is connected, in series with a capacitor of capacitance 50 π x μ F , with 200 V , 50 Hz AC source. The value of x will be _____ .

Step-by-step solution

Electrical power is given by P = V 2 R ⇒ R = V 2 P Resistance of lamp is R = 100 × 100 50 ⇒ R = 200   Ω Let V C and V R be the voltage across capacitor and resistor. Here, V R 2 + V C 2 = V 2 Current through lamp is i = 100 200 = 1 2   A ⇒ 100 2 + V C 2 = 200 2   ⇒ V C 2 = 30000 ⇒ V C = 100 3   V We know that, V = i × X C   Then, X C = 200 3   Ω = 1 ωC So, capacitance of capacitor is C = 1 20 × 50 × 20 3 = 50 × 10 -