Question

A series LCR circuit (L = 10 H, C = 10 µF, R = 50 Ω) is connected to V = 200 sin⁡ (100t). If ν₀​ is the resonant frequency and ν is the source frequency, then ______.

Options

• v₀ = v = 50 Hz

• v₀ = v = \[\frac {50}{π}\]Hz

• v₀ = \[\frac {50}{π}\]Hz, v = 50 Hz

• v = 100 Hz, v₀ = \[\frac {100}{π}\]Hz

Answer 1

A series LCR circuit (L = 10 H, C = 10 µF, R = 50 Ω) is connected to V = 200 sin⁡ (100t). If ν₀​ is the resonant frequency and ν is the source frequency, then v₀ = v = \[\frac {50}{π}\]Hz.

Explanation:

Given: L = 10 H, C = 10 mF,

R = 50 Ω

V = 200 sin (100t)

The standard equation is V = V₀ sin ωt

Hence, ω = 100 rad/s

v = \[\frac{\omega}{2\pi}=\frac{100}{2\pi}=\frac{50}{\pi}\]

v₀ = \[\frac{1}{2\pi\sqrt{LC}}\]

= \[\frac{1}{2\pi}\sqrt{\frac{1}{10\times10\times10^{-6}}}\]

= \[\frac{1}{2\pi}\times\sqrt{\frac{1}{10^{-4}}}\]

= \[\frac{1}{2\pi}\times10^{2}=\frac{50}{\pi}\]

v = v₀ = \[\frac {50}{π}\]Hz