First slide

Electrical Resonance series circuit

Question

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitor. Then what is the value of capacitance?

Moderate

A

$2 \times 10^{- 6} F$
B

$3 \times 10^{- 6} F$
C

$10^{- 4} F$
D

$10^{- 6} F$

Solution

Given in the question :
Inductance = 10 H
Frequency of fan = 50 Hz
We know Resonance is the condition in which maximum power is achieved in an LR circuit.
Thus, for maximum power in LR circuit : X_L = X_C
$ω L = \frac{1}{ω C}$
$\Rightarrow C = \frac{1}{ω^{2} L} = \frac{1}{4 π^{2} f^{2} L}$
$(\sin c e ω = 2 π f)$
$C = \frac{1}{4 \times 10 \times (50)^{2} \times 10} = 10^{- 6} F$

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