Suppose the frequency of the source in the previous example can be varied. (a) What is the frequency of the source at which resonance occurs? (b) Calculate the impedance, the current, and the power dissipated at the resonant condition.
Example-(7.9)
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(a) The frequency at which the resonance occurs is
$
\begin{aligned}
\omega_0 & =\frac{1}{\sqrt{L C}}=\frac{1}{\sqrt{25.48 \times 10^{-3} \times 796 \times 10^{-6}}} \\
& =222.1 rad / s \\
v_r & =\frac{\omega_0}{2 \pi}=\frac{221.1}{2 \times 3.14} Hz =35.4 Hz
\end{aligned}
$
(b) The impedance $Z$ at resonant condition is equal to the resistance:
$
Z=R=3 \Omega
$
The rms current at resonance is
$
=\frac{V}{Z}=\frac{V}{R}=\left(\frac{283}{\sqrt{2}}\right) \frac{1}{3}=66.7 A
$
The power dissipated at resonance is
$
P=I^2 \times R=(66.7)^2 \times 3=13.35 kW
$
You can see that in the present case, power dissipated at resonance is more than the power dissipated in Example 7.8.
$
\begin{aligned}
\omega_0 & =\frac{1}{\sqrt{L C}}=\frac{1}{\sqrt{25.48 \times 10^{-3} \times 796 \times 10^{-6}}} \\
& =222.1 rad / s \\
v_r & =\frac{\omega_0}{2 \pi}=\frac{221.1}{2 \times 3.14} Hz =35.4 Hz
\end{aligned}
$
(b) The impedance $Z$ at resonant condition is equal to the resistance:
$
Z=R=3 \Omega
$
The rms current at resonance is
$
=\frac{V}{Z}=\frac{V}{R}=\left(\frac{283}{\sqrt{2}}\right) \frac{1}{3}=66.7 A
$
The power dissipated at resonance is
$
P=I^2 \times R=(66.7)^2 \times 3=13.35 kW
$
You can see that in the present case, power dissipated at resonance is more than the power dissipated in Example 7.8.
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