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JEE Main 2022 (27 Jun, Shift 1) · AC Basics: Peak, RMS & Average Values

AC Basics: Peak, RMS & Average Values question from JEE Main 2022 (27 Jun, Shift 1)

Q28JEE Main 2022 · 27 JUN · SHIFT 1Difficult

AC Basics: Peak, RMS & Average Values

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 975

Lamp at full brightness: $I = \frac{P}{V} = \frac{5}{25} = 0.2$ A and $R_{lamp} = \frac{V^2}{P} = \frac{625}{5} = 125\ \Omega$ .
Total resistance needed: $R_{total} = \frac{220}{0.2} = 1100\ \Omega$ .
$R = 1100 - 125 = 975\ \Omega$
So $R = 975\ \Omega$ .

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