(B) The power in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$. Given $P = 1000 \,W$ and the peak voltage $V_0 = 200 \,V$. The $r.m.s.$

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(B) The power in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$. Given $P = 1000 \,W$ and the peak voltage $V_0 = 200 \,V$. The $r.m.s.$ voltage is $V_{rms} = \frac{V_0}{\sqrt{2}} = \frac{200}{\sqrt{2}} \,V$. Assuming the lamps are purely resistive, the phase angle $\phi = 0^{\circ}$, so $\cos \phi = 1$. Thus, $1000 = \left( \frac{200}{\sqrt{2}} \right) I_{rms} \times 1$. $I_{rms} = \frac{1000 \times \sqrt{2}}{200} = 5 \sqrt{2} \,A$.

Class 12 Physics Alternating Current Alternating Current, Voltage (rms and Average)

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$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

MHT CET 2023 All MHT CET

A
$10 \,A$
B
$5 \sqrt{2} \,A$
C
$20 \,A$
D
$10 \sqrt{2} \,A$

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Alternating Current

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Alternating Current, Voltage (rms and Average)

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$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

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