Question

For the series L-C-R circuit shown in the figure, the resonance frequency and the current at the resulting resonating frequency will be

• A. $2500rad/s,5\sqrt{2}A$
• B. $2500rad/s,5A$
• C. $2500rad/s,\frac{5}{\sqrt{2}}A$
• D. $25rad/s,5\sqrt{2}A$

Answer 1

The correct option is B $2500rad/s,5A$

For an AC resonant circuit, resonant frequency is given by
$w_0=\frac{1}{\sqrt{LC}}{w}_0=\frac{1}{\sqrt{(8\times {10}^{-3})\times (20\times {10}^{-6})}}=2500rad/s$

For a series resonant circuit, inductive and capacitive reactance cancel each other out and net resistance is only because of resistance which is $R\left(44\Omega \right)$.
So, total current in a circuit is given by
$i=\frac{V}{R}=\frac{220}{44}=5A$