Question

A voltage of 100v,50 hz is applied to a series circuit consists of R= 50 ohms and L=20mH then the current in R is

Answer 1

$Given,</p><p></p><p>RMS voltage, V = 100 v</p><p></p><p>frequency, f = 50 hz</p><p></p><p>Resistance, R = 20 ohm</p><p></p><p>Inductor,L = 20 mh</p><p></p><p>                 = 0.02 h</p><p></p><p>inductive reactance can be given by</p><p></p><p>X_L\ =\ 2.\pi f. LXL = 2.πf.L</p><p></p><p>        =2 x 3.14 x 50 x 0.02</p><p></p><p>        = 6.28 ohm</p><p></p><p>Hence, impedance of the circuit can be given by</p><p></p><p>Z\ =\ R\ +\ X_LZ = R + XL</p><p></p><p>    = 20 + j6.28</p><p></p><p>|Z|=\ \sqrt{\(20)^2+(6.28)^2}</p><p></p><p>    = 20.96 ohm</p><p></p><p>Hence, total impedance of the circuit is 20.96 ohm.</p><p></p><p>Rms current can be given by</p><p></p><p>I_{rms}\ =\ \dfrac{V}{|Z|}Irms = ∣Z∣V</p><p></p><p>             = 4.77 A</p><p></p><p>Hence, RMS value of current is 4.77 A.</p><p></p><p>$