Question

a parallel L-C circuit comprises of a 5H inductor and 5 mu f capacitor. Calculate resonant frequency​

Answer 1

Answer:

The resonant frequency is 31.8 Hz .

Explanation:

Given as :

For L-C circuit

The inductance = L = 5 H

The capacitance = C = 5 $\mu$f

Let The resonant frequency = f Hz

According to question

At resonant condition

Inductive reactant = Capacitive reactant

i.e $X_L$  =  $X_C$

Or, Lω = $\dfrac{1}{C \omega }$

Or, ω² = $\dfrac{1}{LC}$

Or, ω² = $\dfrac{1}{5\times 5\times 10^{-6} }$

Or,  ω² = $\dfrac{10^{6}}{25}$

Or, ω² = 40,000

∴  ω = √40,000

i.e ω = 200 Hz

So, The angular frequency =  ω = 200 Hz

Again

∴ ω = 2 π f

Or, 200 Hz = 2 × 3.14 × f

or, 200 Hz = 6.28 × f

∴   f = $\dfrac{200}{6.28}$

i.e f = 31.8 Hz

So, The resonant frequency = f = 31.8 Hz

Hence, The resonant frequency is 31.8 Hz . Answer