Question

The frequencies at which the current amplitude in an LCR series circuit becomes `1/sqrt2` times its maximum value are 212 rad s^-1 and 232 rad^-1. The value of resistance in the circuit is R = 5Ω. The self inductance in the circuit is ______ mH.

Options

• 150

• 250

• 350

• 450

Answer 1

The frequencies at which the current amplitude in an LCR series circuit becomes `1/sqrt2` times its maximum value are 212 rad s^-1 and 232 rad^-1. The value of resistance in the circuit is R = 5Ω. The self inductance in the circuit is 250 mH.

Explanation:

Band width, Δω = ω₂ - ω₁ = `"R"/"L"` = 232 - 212 = `"R"/"L"`

⇒ 20 = `"R"/"L"` ⇒ L = `"R"/20 = 5/20` = 250 mH