Question

In a series $LCR$ circuit the frequency of a $10V,AC$ voltage source id adjusted in such a fashion that the reluctance of the inductor or measures $15\Omega$ and that of the capacitor $11\Omega$. If $R=3\Omega$, the potential difference across the series combination of $L$ and $C$ will be:

• A. $8V$
• B. $10V$
• C. $22V$
• D. $52V$

Answer 1

The correct option is A $8V$

$i\frac{V_{rms}}{\sqrt{R^2+(X_2–X_1{)}^2}}$

$i=\frac{10}{\sqrt{(3{)}^2+(15-11{)}^2}}$

$i=2A$

$V_R=iR=2\times 3=6V$

$V_L=2\times 15=30V$

$V_L=22V$

$V_L–V_C$

$=30-22$

$=8V$