Practice portal › Alternating Current › Series LCR: Impedance and Phase

A coil of inductance L and resistance R is connected to an A.C. source of V volt. If the angular frequency of the A.C. source is ω rad s⁻¹, then the current in the circuit will be _______.

Asked in GSEB Board March 2018 · Current in a series LCR

• (1) V/R
• (2) V/(ω L)
• (3) V/(R+ω L)
• (4) V/(√R²+ω²L²)

Step-by-step solution

Why the other options are wrong

• (1) Ignores the inductive reactance. V/R is the current only for d.c., where ω=0.
• (2) Ignores the resistance, treating the coil as a pure inductor. A real coil has both R and ω L.
• (3) Adds R and ω L like ordinary numbers. The voltage across L is 90° ahead of the voltage across R, so they combine at right angles: Z=√R²+ω²L².

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