Question

The time constant of an inductance coil is $2.0\times {10}^{-3}$s. When a $90\Omega$ resistance is joined in series, the time constant becomes $0.5\times {10}^{-3}$s.The inductance and resistance of the coil are :-

• A. $30mH$; $30\Omega$
• B. $30mH$; $60\Omega$
• C. $60mh$; $30\Omega$
• D. $60mH$; $60\Omega$

Answer 1

Answer: (C)

$60mh$; $30\Omega$

The time constant of the $L-R$ circuit,

$\frac{L}{R}=2\times {10}^{-3}sec$

$L=2R\times {10}^{-3}H$. . . . . .(1)

When a $90\Omega$ resistance is joined in series, time constant is

$\frac{L}{90+R}=0.5\times {10}^{-3}s$

$\frac{2R\times {10}^{-3}}{90+R}=0.5\times {10}^{-3}$ (from equation 1)

$\frac{2R}{90+R}=0.5$

$2R=0.5(90+R)$

$2R=0.5\times 90+0.5R=45+0.5R$

$1.5R=45$

$R=\frac{45}{1.5}=30\Omega$

From equation (1),

$L=2R=2\times 30\times {10}^{-3}$

$L=60mH$

The correct option is C.