In an RC AC circuit,the maximum voltage and m | vedclass

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(B) The power consumed in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$. Given: $V_{m} = 100 \ V$,$I_{m} = 1.1 \ A$,$X_{C} = 60 \ \Omega

Vedclass · Accepted Answer

$44.0$

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(B) The power consumed in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$. Given: $V_{m} = 100 \ V$,$I_{m} = 1.1 \ A$,$X_{C} = 60 \ \Omega$,$R = 80 \ \Omega$. The impedance $Z$ is calculated as $Z = \sqrt{R^{2} + X_{C}^{2}} = \sqrt{80^{2} + 60^{2}} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \ \Omega$. The power factor is $\cos \phi = \frac{R}{Z} = \frac{80}{100} = 0.8$. The $rms$ values are $V_{rms} = \frac{V_{m}}{\sqrt{2}}$ and $I_{rms} = \frac{I_{m}}{\sqrt{2}}$. Substituting these into the power formula: $P = \left(\frac{100}{\sqrt{2}}ight) 	imes \left(\frac{1.1}{\sqrt{2}}ight) 	imes 0.8$ $P = \frac{100 	imes 1.1}{2} 	imes 0.8$ $P = 50 	imes 1.1 	imes 0.8 = 55 	imes 0.8 = 44.0 \ W$.

In an $RC$ $AC$ circuit,the maximum voltage and maximum current are $100 \ V$ and $1.1 \ A$ respectively. If $X_{C} = 60 \ \Omega$ and $R = 80 \ \Omega$,then the power consumed in the circuit will be . . . . . . . (in $W$)

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