Question

The rms value of the current i(t) in the circuit shown below is

• A. $\frac{1}{2}A$
• B. $\frac{1}{\sqrt{2}}A$
• C. 1 A
• D. $\sqrt{2}A$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}A$

$V_s=V_{m}sin\omega t$ = 1 sint

$V_m=1Vand\omega =1rad/sec$

Impedance of the branch containing inductor and capacitor

$Z=j(X_L-X_C)$

$=j(\omega L-\frac{1}{\omega C})$

$=j(1\times 1-\frac{1}{1\times 1})=0$

So, this branch is short-circuited and the whole currrent flow through it

$i\left(t\right)=\frac{1sint}{1}=1sint$

Rms value of the current
$=\frac{i_m}{\sqrt{2}}$

$=\frac{1}{\sqrt{2}}A$