Question

A box $P$ and a coil $Q$ are connected in series with an $10\text{V}$$\text{AC}$ source of variable frequency. Box $P$ contains a capacitance of $1\mu \text{F}$ in series with a resistance of $32\Omega$. Coil $Q$ has a self inductance of $4.9\text{mH}$ and a resistance of $68\Omega$ in series. The frequency is adjusted so that maximum current flows in $P\text{and}Q$.


$\left(iv\right)$ The voltage across coil $Q$ is

​​​​​​​$[$1 Mark$]$

• A. $20\text{V}$
• B. $\frac{\sqrt{1350}}{10}V$
• C. $5.5\text{V}$
• D. $\frac{\sqrt{9524}}{10}\text{V}$

Answer 1

The correct option is D $\frac{\sqrt{9524}}{10}\text{V}$

Current through the circuit, $I=\frac{V}{Z}$
At resonance,
$Z=R\Rightarrow I=\frac{V}{R}=\frac{10}{(32+68)}=0.1\text{A}$

Voltage across $Q$,
$V_Q=I{Z}_Q=0.1\times \sqrt{9524}$
$V_Q=\frac{\sqrt{9524}}{10}\text{V}$
$\therefore$ option $\left(d\right)$ is correct.