Question

An RLC circuit is composed of a 3.5 kΩ resistor, 1.1 nF capacitor and 7.6 mH inductor. If an AC 6.8 V rms is applied, what frequency (in Hz) is necessary for the maximum power to be supplied to the circuit?

Answer 1

Answer:

$5.5\times 10^{4}$ Hz

Explanation:

we know that the power is maximum in RLC circuit when inductive reactance and capacitive reactance are equal.

$C$ = Capacitance of the capacitor = 1.1 x 10⁻⁹ F

$L$ = Inductance of the inductor = 7.6 x 10⁻³ H

$f$ = frequency necessary for maximum power

$X_{C}$ =  capacitive reactance = $\frac{1}{2\pi fC}$

$X_{L}$ =  inductive reactance = $2\pi fL$

For maximum power :

$X_{L}$ = $X_{C}$

$2\pi fL$ = $\frac{1}{2\pi fC}$

$f = \frac{1}{2\pi \sqrt{LC}}$

$f = \frac{1}{2(3.14) \sqrt{(7.6\times 10^{-3})(1.1\times 10^{-9})}}$

$f =5.5\times 10^{4}$ Hz