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(A) Given: $V_{R} = 80 \, V$,$V_{C} = 40 \, V$,$V_{L} = 100 \, V$.The power factor of an $L-C-R$ circuit is given by $\cos \phi = \frac{R}{Z}$.Since $

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$0.8$

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(A) Given: $V_{R} = 80 \, V$,$V_{C} = 40 \, V$,$V_{L} = 100 \, V$.The power factor of an $L-C-R$ circuit is given by $\cos \phi = \frac{R}{Z}$.Since $V = IZ$ and $V_{R} = IR$,we can write $\cos \phi = \frac{V_{R}}{V}$.The total voltage $V$ in an $L-C-R$ circuit is $V = \sqrt{V_{R}^{2} + (V_{L} - V_{C})^{2}}$.Substituting the given values:$V = \sqrt{80^{2} + (100 - 40)^{2}}$$V = \sqrt{80^{2} + 60^{2}}$$V = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \, V$.Now,calculate the power factor:$\cos \phi = \frac{V_{R}}{V} = \frac{80}{100} = 0.8$.

The potential differences across the resistance,capacitance,and inductance are $80 \, V$,$40 \, V$,and $100 \, V$ respectively in an $L-C-R$ circuit. The power factor of this circuit is:

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