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(B) The power consumed in an $A$.$C$. circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\cos \phi$ is the power factor.Given: $P = 1500 \ W$,

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$8$

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(B) The power consumed in an $A$.$C$. circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\cos \phi$ is the power factor.Given: $P = 1500 \ W$,$V_{rms} = 250 \ V$,$I_{rms} = 10 \ A$.Substituting the values: $1500 = 250 	imes 10 	imes \cos \phi$.$1500 = 2500 \cos \phi \implies \cos \phi = \frac{1500}{2500} = \frac{3}{5} = 0.6$.Since $\sin^2 \phi + \cos^2 \phi = 1$,we have $\sin \phi = \sqrt{1 - (0.6)^2} = \sqrt{1 - 0.36} = \sqrt{0.64} = 0.8 = \frac{4}{5}$.The wattless current is given by $I_{wattless} = I_{rms} \sin \phi$.$I_{wattless} = 10 	imes 0.8 = 8 \ A$.

$A$ circuit,consisting of an inductance and a resistance in series,is connected to a $250 \ V$ $A$.$C$. supply. It draws a current of $10 \ A$. If the power consumed in the circuit is $1500 \ W$,calculate the wattless current. (in $A$)

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