An inductance of 0.2 H and resistance of 100 | vedclass

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(C) Given: Inductance $L = 0.2 \ H$,Resistance $R = 100 \ \Omega$,Voltage $V_{rms} = 180 \ V$,Frequency $f = 50 \ Hz$.First,calculate the inductive re

Vedclass · Accepted Answer

$1.522$

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(C) Given: Inductance $L = 0.2 \ H$,Resistance $R = 100 \ \Omega$,Voltage $V_{rms} = 180 \ V$,Frequency $f = 50 \ Hz$.First,calculate the inductive reactance $X_L = 2 \pi f L$.$X_L = 2 	imes \pi 	imes 50 	imes 0.2 = 20 \pi \ \Omega$.Using $\pi^2 = 10$,we approximate $\pi \approx \sqrt{10} \approx 3.162$.So,$X_L = 20 	imes 3.162 = 63.24 \ \Omega$.The impedance $Z$ of the $RL$ series circuit is $Z = \sqrt{R^2 + X_L^2}$.$Z = \sqrt{100^2 + (63.24)^2} = \sqrt{10000 + 3999.3} = \sqrt{13999.3} \approx 118.32 \ \Omega$.The $RMS$ current $I_{rms} = \frac{V_{rms}}{Z}$.$I_{rms} = \frac{180}{118.32} \approx 1.5213 \ A$.Rounding to three decimal places,we get $1.522 \ A$.

An inductance of $0.2 \ H$ and resistance of $100 \ \Omega$ are connected in series to an $AC$ of $180 \ V$,$50 \ Hz$ supply. The $RMS$ current flowing in the circuit will be . . . . . . (Take $\pi^2$ as $10$). (in $A$)

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