A series LCR circuit with R = 20Ω, L = 1.5H and C = 35μF is connected to a variable-frequency 200V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
Exercise
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At resonance, the frequency of the supply power equals the natural frequency of the given LCR circuit.
Resistance, $\text{R}=20\Omega$
Inductance, L = 1.5H
Capacitance, $C = 35μF = 30 \times 10^{-6}F$
AC supply voltage to the LCR circuit, V = 200V
Impedance of the circuit is given by the relation,
$\text{Z}=\sqrt{\text{R}^2+\Big(\omega\text{L}-\frac{1}{\omega\text{C}}\Big)^2}$
At resonance, $\omega\text{L}=\frac{1}{\omega\text{C}}$
$\therefore\ \text{Z}=\text{R}=20\Omega$
Current in the circuit can be calculated as:
$\text{I}=\frac{\text{V}}{\text{Z}}$
$=\frac{200}{20}=10\text{A}$
Hence, the average power transfer-red to the circuit in one complete cycle= VI
= 200 × 10 = 2000W.
Resistance, $\text{R}=20\Omega$
Inductance, L = 1.5H
Capacitance, $C = 35μF = 30 \times 10^{-6}F$
AC supply voltage to the LCR circuit, V = 200V
Impedance of the circuit is given by the relation,
$\text{Z}=\sqrt{\text{R}^2+\Big(\omega\text{L}-\frac{1}{\omega\text{C}}\Big)^2}$
At resonance, $\omega\text{L}=\frac{1}{\omega\text{C}}$
$\therefore\ \text{Z}=\text{R}=20\Omega$
Current in the circuit can be calculated as:
$\text{I}=\frac{\text{V}}{\text{Z}}$
$=\frac{200}{20}=10\text{A}$
Hence, the average power transfer-red to the circuit in one complete cycle= VI
= 200 × 10 = 2000W.
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