Question

In a series LCR circuit R = 300 Ω, L = 0.9 H, C = 2µF, ω = 1000 rad/s. The impedance of the circuit is ______.

पर्याय

• 500 Ω

• 1300 Ω

• 400 Ω

• 900 Ω

Answer 1

In a series LCR circuit R = 300 Ω, L = 0.9 H, C = 2µF, ω = 1000 rad/s. The impedance of the circuit is 500 Ω.

Explanation:

Impedance for series LCR circuit is given by Z = `sqrt("R"^2 + (omega"L" - 1/(omega"C"))^2)`

Given, resistance, R = 300 Ω, inductance, L = 0.9 H, capacitance, C = 2µF = 2 × 10^-6 F and angular frequency, ω = 1000 rad/s.

Substituting the given values in the above equation, we get

`=> "Z" = sqrt(300^2 + (100 xx 0.9 - 1/(1000 xx 2 xx 10^-8))^2)`

`=> "Z" = sqrt(90000 + (900 - 500)^2)`

`=> "Z"  = sqrt(250000)`

= 500 Ω

Hence, the impedance of LGR circuit is 500 Ω.