1. Tardigrade
  2. Question
  3. Physics
  4. In an AC circuit, a capacitor of capacitance C=(25/π) μ F and a resistor of resistance R=300 Ω are connected in series with an AC source of 200 V and 50 s -1 frequency. The power dissipated (in watt) in the circuit will be

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Q. In an $AC$ circuit, a capacitor of capacitance $C=\frac{25}{\pi} \mu F$ and a resistor of resistance $R=300\, \Omega$ are connected in series with an AC source of $200\, V$ and $50\, s ^{-1}$ frequency. The power dissipated (in watt) in the circuit will be

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Solution:

$\cos \phi=\frac{R}{Z}=\frac{R}{\sqrt{X_{C}^{2}+R^{2}}}=\frac{300}{500}=0.6$
$P=V_{ \text{rms }} i_{\text{ rms }} \cos \phi$
$=\frac{V_{ \text{rms} }^{2}}{z} \cos \phi=\frac{(200)^{2}}{500} \times 0.6=48 W$