Question

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance X_L = 250 πΩ, and an unknown capacitor. The value of capacitance to maximize the average power should be ______.

Options

• 4 μF

• 25 μF

• 40 μF

• 400 μF

Answer 1

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance X_L = 250 πΩ, and an unknown capacitor. The value of capacitance to maximize the average power should be 4 μF.

Explanation:

Given, V = 300 V, f = 50 Hz

R = 3k Ω

X_L = 250 πΩ

Here, it is important to maximize the circuit's average power.

With a series resonance circuit, the impedance is as low as possible, allowing us to increase power.

`Z = sqrt(R^2 + (X_L - X_C)^2)`

Z = Z_min if X_L = X_C

`X_L = X_C = 1/(omegaC)`

⇒ C = `1/(omegaX_L)`

= `1/(2pi xx 50 xx 250pi)`

C = `0.04 xx 10^-4`

= 4 μF