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An electric bulb rated 100 W--220 V is connected to an a.c. source of r.m.s. voltage 220 V. The peak value of the current through the bulb is

Asked in JEE Main 3rd April 2nd Shift 2025 · RMS and mean values

(1) 0.45 A
(2) 2.2 A
(3) 0.64 A
(4) 0.32 A

Answer: (3) 0.64 A

Step-by-step solution

R.m.s. current Iᵣₘₛ=P/V=(100)/(220)=0.4545 A.

Peak current I₀=√2 Iᵣₘₛ=1.414×0.4545≈0.64 A.

Why the other options are wrong

(1) Gives the r.m.s. current 0.45 A, forgetting the ×√2 to reach the peak.
(2) Computes (220)/(100) (voltage and power swapped).
(4) Divides the r.m.s. current by √2 instead of multiplying.

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