$A$ pure inductor of $25.0 \; mH$ is connected to a source of $220 \; V$. Find the inductive reactance and rms current in the circuit if the frequency of the source is $50 \; Hz$.
(A) The inductive reactance $X_L$ is given by the formula $X_L = 2 \pi \nu L$.
Given: $L = 25.0 \; mH = 25 \times 10^{-3} \; H$,$\nu = 50 \; Hz$,and $V_{rms} = 220 \; V$.
Substituting the values: $X_L = 2 \times 3.14 \times 50 \times 25 \times 10^{-3} \; \Omega = 7.85 \; \Omega$.
The rms current $I_{rms}$ is given by $I_{rms} = \frac{V_{rms}}{X_L}$.
Substituting the values: $I_{rms} = \frac{220 \; V}{7.85 \; \Omega} \approx 28.03 \; A$.
Given: $L = 25.0 \; mH = 25 \times 10^{-3} \; H$,$\nu = 50 \; Hz$,and $V_{rms} = 220 \; V$.
Substituting the values: $X_L = 2 \times 3.14 \times 50 \times 25 \times 10^{-3} \; \Omega = 7.85 \; \Omega$.
The rms current $I_{rms}$ is given by $I_{rms} = \frac{V_{rms}}{X_L}$.
Substituting the values: $I_{rms} = \frac{220 \; V}{7.85 \; \Omega} \approx 28.03 \; A$.
Explore More
Similar Questions
Obtain the formula for current when an $AC$ voltage is applied to a capacitor and draw the graphs of $V$ and $I$ versus $\omega t$.
Medium
View SolutionThe reactance of an inductor at $50 \, Hz$ is $10 \, \Omega$. The reactance of it at $200 \, Hz$ is
$A$ $120 \, V$ $AC$ source is connected across a pure inductor of inductance $0.70 \, H$. If the frequency of the source is $60 \, Hz$,the current passing through the inductor is: (in $, A$)
Easy
View SolutionThe graphs given below depict the dependence of two reactive impedances $X_1$ and $X_2$ on the frequency of the alternating e.m.f. applied individually to them. We can then say that
Medium
View SolutionAn $AC$ alternating $emf$ $E = 110 \sqrt{2} \sin(100t) \text{ V}$ is applied to a capacitor of $2 \mu F$. The $rms$ value of current in the circuit is $...... \text{ mA}$.
DifficultJEE MAIN 2024
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo