What is the value of inductance L for which the current is a maximum in a series L C R circuit with C=10 F and =1000 ~s ⁻¹ ?

Step-by-step solution

Current in L C R series circuit, i= V R²+ (X_ L -X_ C )² where V is rms value of current, R is resistance, X_ L is inductive reactance and X_ C is capacitive reactance. For current to be maximum, denominator should be minimum which can be done, if X_ L =X_ C This happens in resonance state of the circuit ie, L= 1 C or L= 1 ² C ...(i) aligned Given, &=1000 ~s ⁻¹, C=10 F &=10 10⁻⁶ ~F Hence, L &= 1 (1000)² 10 10⁻⁶ &=0.1 H &=100 mH aligned