Question

A series $RLC$ circuit, driven with $E_{rms}=120V$ at frequency $50Hz$ , contains an inductance with $X_L=100\Omega$ , a capacitance with $X_c=110\Omega$ and an unknown resistance $R$ . For what value of $R$ , the power factor is $0.9$ ?

• A. $20\Omega$
• B. $42\Omega$
• C. $59\Omega$
• D. $110\Omega$

Answer 1

Answer: (A)

Given, $E_{rms}=120V$
$f=50Hz$
$X_L=100\Omega$
$X_c=110\Omega$
Power factor $=0.9$
To find $R$ = ?
As power factor in $LCR$ circuit
$\cos \varphi =\frac{R}{\sqrt{R^2+{\left(\omega L-\frac{1}{\omega C}\right)}^2}}$
$0.9=\frac{R}{\sqrt{R^2+{\left(100-110\right)}^2}}$
$0.9=\frac{R}{\sqrt{R^2+100}}$
$\Rightarrow 0.81=\frac{R^2}{R^2+100}$
$\Rightarrow R=20\Omega$