QJEEM20Ph3bfb: JEE Main 2020 Physics - Class 12 JEEM20Ph3bfb Solution: An inductance coil has a reactance of 100 Ω . When an AC signal …

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An inductance coil has a reactance of 100

Ω

. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45^o. The self-inductance of the coil is

Accepted Answer

L-R circuit :

tan 45^o =

\frac{X_{L}}{R}

\Rightarrow

1 =

\frac{X_{L}}{R}

\Rightarrow

X_L = R

Now Z =

\sqrt{R^{2} + X_{L}^{2}}

or Z =

\sqrt{X_{L}^{2} + X_{L}^{2}} = \sqrt{2 X_{L}^{2}}

=

\sqrt{2} X_{L}

\Rightarrow

100 =

\sqrt{2} X_{L}

X_L =

\frac{100}{\sqrt{2}}

\Rightarrow

ω L

=

\frac{100}{\sqrt{2}}

\Rightarrow

L =

\frac{100}{\sqrt{2} \times 2 \times 3.14 \times 1000}

= 1.1

\times

10^–2 H

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