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In an L–R A.C. circuit, at time t the current is I and the time rate of change of current is (dI)/(dt). What will be the potential difference between the two ends of the inductor?

Asked in GSEB Board July 2015 · Behaviour of R, L and C separately

• (1) L(dI)/(dt)
• (2) 1/L(dI)/(dt)
• (3) LI
• (4) L/I

Step-by-step solution

Why the other options are wrong

• (2) Dividing by L turns the relation upside down. A larger inductance opposes the same change of current more strongly, so the voltage grows with L: V_L=L(dI)/(dt).
• (3) LI is the magnetic flux linked with the coil, Φ=LI, not a voltage. The voltage is the rate of change of that flux, (d(LI))/(dt)=L(dI)/(dt).
• (4) L/I has no meaning here. The voltage across an inductor depends on how fast the current is changing, not on the value of the current itself.

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