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

`5.5* 10^(4)` Hz

Step-by-step 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 =
`(1)/(2\pi fC)`

`X_(L)` = inductive reactance =
`2\pi fL`

For maximum power :

`X_(L)` =
`X_(C)`

`2\pi fL` =
`(1)/(2\pi fC)`

`f = (1)/(2\pi √(LC))`

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

`f =5.5* 10^(4)` Hz