A series LCR circuit contains inductance 5 mH, capacitance `2 mu F` and resistance `10 Omega`. If a frequency A.C. source is varied, what is the frequency at which maximum power is dissipated ?

Options

A. `2/pi xx 10^(5)` Hz
B. `(10^(5))/(pi)` Hz
C. `5/pi xx 10^(3)` Hz
D. `(10^(-5))/(pi)` Hz

Answer

C

Explanation

Maximum power is dissipated at resonant frequency.
Resonant frequency, `upsilon_(r)=(1)/(2 pi sqrt(LC))`
Here, `L=5 mH = 5xx10^(-3)H`
`C=2 mu F = 2 xx 10^(-6)F`
`:.upsilon_(r)=(1)/(2 pi sqrt(5xx10^(-3)xx2xx10^(-6)))=(1)/(2 pi sqrt(10^(-8)))`
`=(10^(4))/(2 pi)=5/pi xx 10^(-3)`Hz