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 $P\text{and}Q$.


$\left(ii\right)$ The impedance of coil $Q$ at this frequency is

​​​​​​​$[$1 Mark$]$

• A. $200\Omega$
• B. $\sqrt{1350}\Omega$
• C. $55\Omega$
• D. $\sqrt{9524}\Omega$

Answer 1

The correct option is D $\sqrt{9524}\Omega$

As this circuit is a series LCR circuit, current will be maximum at resonance, i.e.
$\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{(4.9\times {10}^{-3})\left({10}^{-6}\right)}}=\frac{{10}^5}{7}\frac{rad}{s}$
Impedance of Q, $Z_Q=\sqrt{R_2^2+X_L^2}$
$=\sqrt{R_2^2+(\omega L{)}^2}$
$=\sqrt{(68{)}^2+{(4.9\times {10}^{-3}\times \frac{{10}^5}{7})}^2}$
$=\sqrt{{68}^2+{70}^2}$
$Z_Q=\sqrt{9524}\Omega$
$\therefore$ $\left(d\right)$ is the correct option.