Question

Consider a circuit shown below,
At steady state, the current through resistor is given by $15cost$ and the voltage across the inductor is $2\sin t$ .
The RMS value of the current through the capacitor is

• A. $\frac{15}{\sqrt{2}}A$
• B. $12\sqrt{2}A$
• C. $7\sqrt{2}A$
• D. $8\sqrt{2}A$

Answer 1

The correct option is C $7\sqrt{2}A$

We know that ,

$V_L\left(t\right)=L\frac{d{i}_L\left(t\right)}{dt}$

$or,i_L\left(t\right)=\frac{1}{L}\int V_L\left(t\right)dt=\frac{1}{2}\int 2sintdt$

$i_L\left(t\right)=-\cos tA$

also,$i_R\left(t\right)=15costA$

By KCL,

$i_R\left(t\right)-i_C\left(t\right)+i_L\left(t\right)=0$

or, $i_C\left(t\right)=i_L\left(t\right)+i_R\left(t\right)$

$=15\cos t-\cos t=14\cos tA$

RMS value of $i_C\left(t\right)=\frac{14}{\sqrt{2}}=7\sqrt{2}A$