First slide

Phasors and Phasor Diagrams

Question

A given LCR series circuit satisfies the condition for resonance with a given AC source. If the angular frequency of the AC source is increased by 100% then in order to establish resonance, without changing the value of inductance, the capacitance must be

Moderate

A

increased by 100%
B

Reduced by 50%
C

increased by 75%
D

reduced by 75%

Solution

wL = $\frac{1}{{\omega c}}$ (for resonance)
${\omega ^2} = \frac{1}{{LC}}$
for case (ii)
${\left( {2\omega } \right)^2} = \frac{1}{{L{C_1}}}$
(ii) divide (i) $\Rightarrow$ 4
= $\frac{C}{{{C_1}}} \Rightarrow {C_1} = \frac{C}{4}$
The capacitance is to be reduced by 75%.

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