91Ó°ÊÓ

An inductor is a passive two-terminal device that stores energy in a magnetic field when current passes through it. When an inductor is attached to an AC supply, the resistance produced by it is called inductive reactance (X_L).

Resistance is measure of opposition to the flow of current in a closed electrical circuit. It is measured in Ohm (Ω).

Series Resistance, R = 150 Ω

The inductance of the coil, L = 0.250 H

Equation of voltage across resistor is

$v_R=\left(3.80v\right)\cos \left[\left(720rad/s\right)t\right]$

By using ohm’s law

$$\begin{gathered} I\frac{v_R}{R} \\ =\left(\frac{3.80v}{150\mathrm{Î\copyright }}\right)\cos \left[\left(720rad/s\right)t\right] \\ =\left(0.025A\right)\cos \left[\left(720rad/s\right)t\right] \end{gathered}$$

Therefore, the expression of circuit current is given by$I=\left(0.025A\right)\cos \left[\left(720rad/s\right)t\right]$

Inductive reactance is given by,

$\begin{array}{l}{x}_L=\mathrm{Ó\neg }L\\ =\left(720rad/s\right)\left(0.250H\right)\\ =180Q\end{array}$

Therefore, the inductive reactance of the inductor is 180 Ω.

Voltage across inductor leads the current by a phase different of – 90 degrees, so the expression of voltage can be given as –

$$\begin{gathered} v_L=V_L\cos \left(\mathrm{Ó\neg }t+90°\right) \\ =I{X}_L\cos \left(\mathrm{Ó\neg }t+90°\right) \\ =\left(0.025A\right)\left(180\mathrm{Î\copyright }\right)\cos \left[\left(720rad/s\right)t+90°\right] \\ =-\left(4.56V\right)\sin \left[\left(720rad/s\right)t\right] \end{gathered}$$

Therefore, the expression of voltage across inductor is$v_L=-\left(4.56V\right)\sin \left[\left(720rad/s\right)t\right]$