Question

An inductance coil is connected to an $ac$ source through a $60\Omega$,resistance in series. The source voltage, voltage across the coil and voltage across the resistance are found to be $33V,27V$ abd $12V$ respectively. Therefore, the resistance of the coil is

• A. $30\Omega$
• B. $45\Omega$
• C. $105\Omega$
• D. $75\Omega$

Answer 1

The correct option is A $30\Omega$

$I=\frac{12}{60}=\frac{1}{5}$

$V_S^2=V_L^2+(V_R+V_{60}{)}^2$

$V_S^2=V_L^2+V_R^2+2V_R{V}_{60}+V_{60}^2$

$(33{)}^2=(27{)}^2+2V_R\left(12\right)+(12{)}^2$

$1089=729+24V_R+144$

$24V_R=216$

$V_R=\frac{216}{24}=9$

$IR=9$

$R=\frac{9}{I}=\frac{1}{\frac{1}{5}}=45\Omega$