Question

An ac-circuit is shown in the figure:
Calculate:
(i) the reactance of the inductance $L$. (ii) the impedance of the total circuit. (iii) the peak value of the current in the circuit. (iv) phase difference between applied voltage and the current in the circuit.

Answer 1

general equation for voltage of A.C. supply ata given time t

$v=asin(\omega t+\varphi )$

and given equation in question

$v=10sin\left(1000t\right)$

comparing these two equations we have

voltage amplitude $a=10$ ,

$\omega =1000$ ,

and $\varphi =0$

1) reactance of inductor $x=L\omega$

so $x\left(inductor\right)=0.1\times 1000$

$x=100\Omega$

2) as the circuit is resistive and inductive only so impedence of circuit is :

$z=(x^2+R^2{)}^{0.5}$

so $z=(10000+10000{)}^{0.5}$

$z=100\times \sqrt{2}$

$z=100\sqrt{2}$

3)peak value of current in circuit $i=\frac{10}{141.4}=0.07A$

4) phase difference $tan\left(\varphi \right)=\frac{x}{R}$

$tan\left(\varphi \right)=\frac{100}{100}=1$

$\varphi ={tan}^{-1}\left(1\right)$