Alternating Current

JEE Main level, numerical answer, medium

108 of 190

Question 108 of 190

Two circuits are shown in figure (a)(a) and (b)(b). At a frequency of _______ rads−1rad{s}^{-1} the average power dissipated in one cycle will be the same in both the circuits.

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Answer: 500

For figure (a)(a)
Pavg=Vrms2R{P}_{avg}=\dfrac{{V}_{rms}^{2}}{R}
vrms2Z2×R=vrms2R×1\dfrac{{v}_{rms}^{2}}{{Z}^{2}}\times R=\dfrac{{v}_{rms}^{2}}{R}\times 1
R2=Z2{R}^{2}={Z}^{2}
25=((xC−xL)2+52)225={\left(\sqrt{{\left({x}_{C}-{x}_{L}\right)}^{2}+{5}^{2}}\right)}^{2}
25=(xc−xL)2+2525={\left({x}_{c}-{x}_{L}\right)}^{2}+25
xc=xL⇒1ωC=ωL{x}_{c}={x}_{L}\Rightarrow \dfrac{1}{\omega C}=\omega L
ω2=1LC=1060.1×40{\omega }^{2}=\dfrac{1}{LC}=\dfrac{{10}^{6}}{0.1\times 40}
ω=500\omega =500

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