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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Electric Circuits In Exercises 33 and 34, use the differential equation for electric circuits given by

L d I d t + R I + E

In tills equation. I is the current, K is the resistance, L is the inductance, and E Is the electromotive force (voltage).

Solve the differential equation for the current given a constant voltage E 0 .

To determine

To calculate: The solution of the differential equation LdIdt+RI+E for the electric circuit where L is the inductance, E is the electro motive force, I is the current, R is the resistance and the Eo is the constant voltage in the electric circuits.

Explanation

Given:

The differential equation for the electric circuit,

LdIdt+RI+E …… (1)

Formula Used:

The linear differential equation of the form:

dIdt+PI=Q

The integrating factor is ePdt

Calculation:

Consider the differential equation LdIdt+RI+E

Divide the equation (1) by L,

dIdt+(RL)I=EL

The obtained equation is a linear differential equation of the form of:

dIdt+PI=Q

For, the integrating factor,

ePdt=eRLdt=eRtL

Now, multiply the equation with the integrating factor on

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