A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L=10 mH) is 31.4 V, then the current in this circuit is _______.

Solution

Physics sir · 3 steps

The inductor's own voltage and its own reactance give the current. The 200 V is not needed here.

1. Same current everywhere. In a series circuit the same current flows through R, L and C. So the current through the inductor is the circuit current.
2. Inductive reactance. With L = 10 mH = 10⁻² H and f = 50 Hz, X_L = 2π f L = 2 × 3.14 × 50 × 10⁻² = 3.14 Ω.

   I = V_L/X_L = (31.4 V)/(3.14 Ω) = 10 A

3. So. The current in the circuit is 10 A, which is option (a).

The idea to keep. In a series circuit, use any one element's voltage with that element's own resistance or reactance to get the current. The source voltage is shared, so it cannot be used across one element alone.

Answer from the NTA final answer key. Solution by PrepWiser.