A capacitor of unknown capacitance, a resistor of 100 $\Omega$ and an inductor of self inductance L = $( 4 /\pi^{2})$henry are connected in series to an ac source of 200V and 50 Hz. Calculate the value of the capacitance and impedance of the circuit when the current is in phase with the voltage. Calculate the power dissipated in the circuit.
CBSE OUTSIDE DELHI - SET 2 SOUTH 2016
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Capacitance = C $ =\frac{1}{\text{L}\omega^{2}}$
$ = \frac{1}{\frac{4}{\pi^{2}}(2\pi\times50)^{2}}\text{F}$
$ = 2.5 \times10^{-5}\text{F}$
Impedence= resistance (since V and I are in phase)
$\therefore\text{Impedence} = 100\Omega$
Power discipated $ =\frac{\text{E}^{2}_{rms}}{\text{R}}$
$ =\frac{(200)^{2}}{100}\text{W} = 400 \text{ watt}$.
$ = \frac{1}{\frac{4}{\pi^{2}}(2\pi\times50)^{2}}\text{F}$
$ = 2.5 \times10^{-5}\text{F}$
Impedence= resistance (since V and I are in phase)
$\therefore\text{Impedence} = 100\Omega$
Power discipated $ =\frac{\text{E}^{2}_{rms}}{\text{R}}$
$ =\frac{(200)^{2}}{100}\text{W} = 400 \text{ watt}$.
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