The variation of current amplitude in a series LCR circuit with the angular frequency of the AC source is plotted. The peak of the curve is observed to occur at an angular frequency of 1000 rad/s . If the inductance of the circuit is 50 mH , the capacitance of the circuit is _____ F .

Step-by-step solution

At the peak of the current amplitude versus angular frequency curve, the circuit is in resonance. The resonant angular frequency is given by ₀ = 1 LC . Given ₀ = 1000 rad/s and L = 50 mH = 50 10⁻³ H . Squaring both sides and rearranging for C : C = 1 ₀^2 L Substituting the given values: C = 1 (1000)^2 50 10⁻³ C = 1 10^6 0.05 = 1 50000 F C = 20 10⁻⁶ F = 20 F . Answer: 20