A series LCR circuit containing 5.0 H inductor, 80 \mu F capacitor and 40 \Omega resistor is connected to 230V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be :

Alternating Current question

2021 · Q167

Alternating Current question

2021 · Q167

View written solutionFree

Correct answer: D

$Q = {\omega \over {\Delta \omega }} = {{\omega L} \over R} \Rightarrow \Delta \omega = R/L = {{50} \over 4} = 8$ rad/sec

${\omega _0} = {1 \over {\sqrt {LC} }} = {1 \over {\sqrt {5 \times 80 \times {{10}^{ - 6}}} }} = 50$ rad/sec

${\omega _{\min }} = {\omega _0} - {{\Delta \omega } \over 2} = 46$ rad/sec

${\omega _{\max }} = {\omega _0} - {{\Delta \omega } \over 2} = 54$ rad/sec

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Alternating Current question

2021 · Q167

Alternating Current question

2021 · Q167

View written solutionFree

Correct answer: D

$Q = {\omega \over {\Delta \omega }} = {{\omega L} \over R} \Rightarrow \Delta \omega = R/L = {{50} \over 4} = 8$ rad/sec

${\omega _0} = {1 \over {\sqrt {LC} }} = {1 \over {\sqrt {5 \times 80 \times {{10}^{ - 6}}} }} = 50$ rad/sec

${\omega _{\min }} = {\omega _0} - {{\Delta \omega } \over 2} = 46$ rad/sec

${\omega _{\max }} = {\omega _0} - {{\Delta \omega } \over 2} = 54$ rad/sec