A series LCR circuit with R = 10 and L = 0.5 H is connected to a variable frequency a.c. source. If the capacitive reactance at the resonant frequency is 50 , the capacitance of the capacitor is _______ F .

Step-by-step solution

At resonance, the capacitive reactance is equal to the inductive reactance, X_C = X_L . We know that at resonance, the angular frequency is _r = 1 LC . Thus, X_C = X_L = _r L = L LC = L C . Squaring both sides, we get: X_C^2 = L C Rearranging for C : C = L X_C^2 Substituting the given values L = 0.5 H and X_C = 50 : C = 0.5 (50)^2 C = 0.5 2500 C = 2 10⁻⁴ F Converting to microfarads: C = 200 10⁻⁶ F = 200 F Answer: 200