How do you obtain the maximum current in a capacitor-inductor circuit?

How do you obtain the maximum current in a capacitor-inductor circuit?

• A. By increasing resistance
• B. By using DC power source
• C. By connecting it to an AC power source with the same frequency
• D. By reducing the capacitance

Answer: (C)

Driving an LC circuit at its resonant frequency minimizes its impedance, which lets the current be as large as possible for a given source. In an LC circuit, the inductive reactance is X_L = ωL and the capacitive reactance is X_C = 1/(ωC). At resonance, ω = ω0 = 1/√(LC), so X_L = X_C and they cancel each other out, leaving the impedance equal to the resistance. With less impedance, the current I = V/R (for a real source with some resistance) becomes maximal. If you use DC, after transients the current dies away; increasing resistance lowers current; changing capacitance moves the resonance but doesn’t inherently maximize current without adjusting the frequency. So the best way to obtain maximum current is to connect it to an AC power source at the resonant frequency.

Driving an LC circuit at its resonant frequency minimizes its impedance, which lets the current be as large as possible for a given source. In an LC circuit, the inductive reactance is X_L = ωL and the capacitive reactance is X_C = 1/(ωC). At resonance, ω = ω0 = 1/√(LC), so X_L = X_C and they cancel each other out, leaving the impedance equal to the resistance. With less impedance, the current I = V/R (for a real source with some resistance) becomes maximal. If you use DC, after transients the current dies away; increasing resistance lowers current; changing capacitance moves the resonance but doesn’t inherently maximize current without adjusting the frequency. So the best way to obtain maximum current is to connect it to an AC power source at the resonant frequency.