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## Homework Statement

Give a definition of (self) inductance. Suppose a battery, which supplies a constant EMF ϵ_0 is connected to a circuit of resistance R and inductance L at t = 0. Find an expression for the current as a function of time.

## Homework Equations

V = IR

[tex] V = -L\frac{dI}{dt} [/tex

## The Attempt at a Solution

I am assuming that this is to be treated as a Kirchoff Loop, thus the total voltage = 0

*Voltage providers:*

Inductor

Battery

*Users:*

Resistor

Thus I have the equation:

[tex] \epsilon - L\frac{dI}{dt} - IR = 0 [/tex]

and thus:

[tex] \epsilon - L\frac{dI}{dt} = IR [/tex]

treating like a differential equation:

[tex] \epsilon - L\frac{dI}{dt} = IR [/tex]

[tex] \epsilon dt - L dI = IR dt [/tex]

rearrange:

[tex] \frac{L}{IR} dI = -dt + \epsilon dt [/tex]

Gives:

[tex] \frac{1}{L}ln(IR) dI = -t + \epsilon t [/tex]

multiply by L

[tex] ln(IR) = -Lt + \epsilon t [/tex

take exponentials:

[tex] IR = e^{-Lt} + e^{\epsilon t} [/tex]

Does this look right so far?

TFM