An A.C. voltage is applied to a pure inductor | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) When an $A.C.$ voltage $V = V_m \sin(\omega t)$ is applied to a pure inductor of inductance $L$,the induced electromotive force $(EMF)$ is given b

Vedclass · Accepted Answer

lags behind the voltage by $(\pi / 2)^c$

Vedclass · Answer

(C) When an $A.C.$ voltage $V = V_m \sin(\omega t)$ is applied to a pure inductor of inductance $L$,the induced electromotive force $(EMF)$ is given by $\varepsilon = -L \frac{di}{dt}$.Applying Kirchhoff's voltage law,$V - L \frac{di}{dt} = 0$,which implies $V = L \frac{di}{dt}$.Substituting $V$,we get $V_m \sin(\omega t) = L \frac{di}{dt}$,so $di = \frac{V_m}{L} \sin(\omega t) dt$.Integrating both sides,$i = \int \frac{V_m}{L} \sin(\omega t) dt = -\frac{V_m}{\omega L} \cos(\omega t) = \frac{V_m}{\omega L} \sin(\omega t - \pi / 2)$.Comparing the phase of voltage $(\omega t)$ and current $(\omega t - \pi / 2)$,it is clear that the current lags behind the voltage by a phase angle of $\pi / 2$ radians.

An $A.C.$ voltage is applied to a pure inductor. The current in the inductor

Similar Questions

The same current is flowing in two alternating circuits. The first circuit contains only an inductor and the other contains only a capacitor. If the frequency of the $AC$ emf is increased,what will be the effect on the value of the current?

In which circuit is the average power consumed maximum?

If the capacitance of a pure capacitor in a $DC$ circuit is $1 \ F$,then what will be its capacitive reactance?

$A$ $44 \; mH$ inductor is connected to $220 \; V, 50 \; Hz$ $ac$ supply. Determine the $rms$ value of the current (in $A$) in the circuit.

When an $A$.$C$. source is connected across a pure capacitor,the correct phase relation between current $(i_c)$ and voltage $(e_c)$ is shown in the figure.

Vedclass Test Series

Exam Paper Generator

Online Exam Module