Problem 2

An ideal DC source of emf

\mathcal E

is connected in series with a resistor

R>0

and ideal inductor

L>0

. Before the switch closes the inductor current is zero; at

t=0

the switch closes, with positive current chosen along the source. Neglect internal resistance and take all elements as constant. (a) Use Kirchhoff's law to find

I(t)

for

t\ge0

. (b) Determine the steady current

I_\infty

. (c) Find when the current reaches

0.90I_\infty

and check the initial and long-time limits.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

I(t)=\frac{\mathcal E}{R}+Ce^{-Rt/L}

problems.proof.analysis

A constant particular solution is $\mathcal E/R$ , while the homogeneous part decays exponentially. Their sum is the general solution.