Question

An L-C-R series circuit containing a resistance of $R=120\Omega$ has angular resonant frequency $4\times {10}^5$ rad/s. At resonance the voltage across resistance and inductance are 60 V and 90 V respectively. Then values of L and C are :

• A. $0.2mH,\frac{1}{16}\mu F$
• B. $0.2mH,\frac{1}{32}\mu F$
• C. $0.4mH,\frac{1}{32}\mu F$
• D. $0.4mH,\frac{1}{16}\mu F$

Answer 1

The correct option is B $0.2mH,\frac{1}{32}\mu F$

$R=120\Omega ,{\omega }_r=4\times {10}^5$ rad/sec
$V_R=60V,V_L=40V$
$V_R=iR\Rightarrow 60=i\times 120$
$i=\frac{1}{2}A$
$V_L=i{X}_L\Rightarrow 40=\frac{1}{2}{X}_L$
$\therefore X_L=80\Omega$
${\omega }_{r}L=80\Rightarrow 4\times {10}^{5}L=80$
$L=20\times {10}^{-5}H=0.2mH$
$X_C=X_L=80\Rightarrow \frac{1}{{\omega }_{r}C}=80$
$C=\frac{1}{80\omega }=\frac{1}{80\times 4\times {10}^5}$
$\frac{{10}^{-6}}{32}=\frac{1}{32}\mu F$