A circuit when connected to an AC source of 12 V gives a current of 0.2 A. The same circuit when connected to

Question

A circuit when connected to an AC source of 12 V gives a current of 0.2 A. The same circuit when connected to a DC source of 12 V, gives a current of 0.4 A. The circuit is:

Accepted Answer

1. **DC Behavior:** When connected to a DC source, the frequency $\omega$ is zero. A capacitor offers infinite reactance ($X_C = 1/\omega C = \infty$) to DC, blocking the current completely . Since a steady current of 0.4 A flows, the circuit cannot contain a capacitor in series. This eliminates options containing C (RC, LC, LCR).
2. **Resistance:** The resistance of the circuit can be calculated using the DC data: $R = V_{DC} / I_{DC} = 12 	ext{ V} / 0.4 	ext{ A} = 30 \, \Omega$ .
3. **AC Behavior:** When connected to an AC source, the circuit offers impedance $Z$. Calculating impedance: $Z = V_{AC} / I_{AC} = 12 	ext{ V} / 0.2 	ext{ A} = 60 \, \Omega$.
4. **Conclusion:** The impedance ($60 \, \Omega$) is greater than the resistance ($30 \, \Omega$). This indicates the presence of a reactive component ($X$) such that $Z = \sqrt{R^2 + X^2}$. Since capacitors are ruled out, the reactive component must be an inductor ($X_L$). Thus, the circuit is a series combination of Inductance (L) and Resistance (R) .

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