JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Alternating Current

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Two circuits are shown in the figure (a) & (b). At a frequency of _____ rad/s the average power dissipated in one cycle will be same in both the circuits.

Answer: 500

Solution

The first circuit contains only the resistance, so its impedance is

R

and the average power drawn from the

220

V supply is

\frac{V _{r m s}^{2}}{R}

. In the series circuit the average power is

\frac{V _{r m s}^{2} R}{Z ^{2}}

with

Z = R^{2} + (ω L - \frac{1}{ω C})^{2}

The two powers are equal when

Z = R

, which requires

ω L = \frac{1}{ω C}

, that is

ω = \frac{1}{L C}

. With

L = 0.1

H and

C = 40 μ

ω = \frac{1}{0.1 \times 40 \times 1 0 ^{- 6}} = \frac{1}{2 \times 1 0 ^{- 3}} = 500

The dissipated power is the same in both circuits at

500

rad/s.

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Integer answer

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