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An inductor of inductance L henry is connected to an A.C. source V = V₀ sin ω t. Then the current flowing through the inductor is I = ______ A.

Asked in RS Academy GUJCET booklet · Behaviour of R, L and C separately

• (1) (V₀)/(ω L)sin (ω t + π/2)
• (2) (V₀)/(ω L)sin (ω t - π/2)
• (3) V₀ ω L sin (ω t - π/2)
• (4) (ω L)/(V₀)sin (ω t + π/2)

Step-by-step solution

Why the other options are wrong

• (1) Right amplitude, wrong phase: a current leading the voltage by π/2 is what a capacitor gives. In an inductor the current lags.
• (3) Right phase, but multiplies by the reactance instead of dividing by it: I₀ = (V₀)/(X_L) = (V₀)/(ω L). This expression is not even in ampere (it is volt times ohm).
• (4) Inverts the amplitude ((ω L)/(V₀) has the unit A⁻¹) and also uses the capacitor's leading phase.

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