1. Tardigrade
  2. Question
  3. Physics
  4. A series LCR-circuit with R = 20 Ω, L = 1.5 H and C = 35 μ F is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

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Q. A series $LCR$-circuit with $R = 20\,\Omega$, $L = 1.5\,H$ and $C = 35\,\mu F$ is connected to a variable frequency $200\,V$ ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

Alternating Current

Solution:

If the frequency of the ac source equals the natural frequency of the circuit, the impedance
$Z=R=20\,\Omega$
The average power dissipated per cycle,
$P_{av}=\frac{V^{2}_{rms}}{Z}$
$=\frac{V^{2}_{rms}}{R}$
$=\frac{\left(200\right)^{2}}{20}$
$=2000\,W$