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AC Voltage Applied to an Inductor

A 100 resistance is connected in series with a 4 H inductor.

Question

Medium

Solving time: 3 mins

A $100Ω$ resistance is connected in series with a $4 H$ inductor. The voltage across the resistor is $V_{R} = (2.0 V) sin (1 0^{3} rad / s) t$ :
(a) Find the expression of circuit current
(b) Find the inductive reactance
(c) Derive an expression for the voltage across the inductor.

Name: Video solution 1: A 100Ω resistance is connected in series with a 4H inductor. The voltage across the resistor is VR=(2.0 V)sin(103rad/s)t :(a) Find the expression of circuit current(b) Find the inductive reactance(c) Derive an expression for the voltage across the inductor.
Uploaded: 2022-11-15T13:21:28.000Z
Duration: 1 min
Description: Video solution 1: A 100Ω resistance is connected in series with a 4H inductor. The voltage across the resistor is VR=(2.0 V)sin(103rad/s)t :(a) Find the expression of circuit current(b) Find the inductive reactance(c) Derive an expression for the voltage across the inductor.

Views: 5,502 students

Updated on: Nov 15, 2022

Book:

Electricity and Magnetism (DC Pandey)

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Mateo Discussed

100Ω

resistance is connected in series with a

4 H

inductor. The voltage across the resistor is

V_{R} = (2.0 V) sin (1 0^{3} rad / s) t

:
(a) Find the expression of circuit current
(b) Find the inductive reactance
(c) Derive an expression for the voltage across the inductor.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

(a)

i = \frac{V _{R}}{R} = \frac{( 2.0 V ) s i n ( 1 0 ^{3} rad / s ) t}{100}

= (2.0 \times 1 0^{- 2} A) sin (1 0^{3} rad / s) t

(b)

X_{L} = ω L = (1 0^{3} rad / s) (4 H)

= 4.0 \times 1 0^{3} Ω

V_{0} = i_{0} X_{L} = (2.0 \times 1 0^{- 2} A) (4.0 \times 1 0^{3} Ω)

= 80 V

In an

AC

, voltage across the inductor leads the current by

9 0^{\circ}

π /2 rad

. Hence,

V_{L} = V_{0} sin (ω t + π /2)

= (80 V) sin {(1 0^{3} rad / s) t + \frac{π}{2} rad}

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Question Text	A $100Ω$ resistance is connected in series with a $4 H$ inductor. The voltage across the resistor is $V_{R} = (2.0 V) sin (1 0^{3} rad / s) t$ : (a) Find the expression of circuit current (b) Find the inductive reactance (c) Derive an expression for the voltage across the inductor.
Updated On	Nov 15, 2022
Topic	Alternating Current
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	116
Avg. Video Duration	1 min

A $100Ω$ resistance is connected in series with a $4 H$ inductor. The voltage across the resistor is $V_{R} = (2.0 V) sin (1 0^{3} rad / s) t$ :
(a) Find the expression of circuit current
(b) Find the inductive reactance
(c) Derive an expression for the voltage across the inductor.

Text solutionVerified

Filo tutor solutions (1)

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A 100Ω resistance is connected in series with a 4H inductor. The voltage across the resistor is VR​=(2.0 V)sin(103rad/s)t :(a) Find the expression of circuit current(b) Find the inductive reactance(c) Derive an expression for the voltage across the inductor.

Text solutionVerified

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A $100Ω$ resistance is connected in series with a $4 H$ inductor. The voltage across the resistor is $V_{R} = (2.0 V) sin (1 0^{3} rad / s) t$ :
(a) Find the expression of circuit current
(b) Find the inductive reactance
(c) Derive an expression for the voltage across the inductor.