The variation of rms current ( I_ rms ) with angular frequency ( ) for a series LCR circuit is plotted. The resulting curve shows that the current reaches its maximum peak value at an angular frequency of 1000 rad/s. If the capacitance in the circuit is 10 F, what is the value of the inductance?

Step-by-step solution

The peak current in a series LCR circuit occurs at the condition of resonance. From the described graph, the angular resonant frequency is _r = 1000 rad/s. The condition for resonance in terms of angular frequency is _r = 1 LC . Squaring both sides and rearranging for inductance L gives: L = 1 _r^2 C Given C = 10 F = 10 10⁻⁶ F = 10⁻⁵ F . Substituting the values: L = 1 (1000)^2 10⁻⁵ L = 1 10^6 10⁻⁵ = 1 10 H L = 0.1 H = 100 mH Answer: 100 mH