Question #306163

In a series RL circuit, L = 4H, R = 100 ohms and E = 200V . Find the values of current as a function of time. Assume that the initial current is zero. Find the current when t = 2 secons.

1
Expert's answer
2022-03-08T15:12:01-0500

Solution;

Using the equation;

Ldidt+Ri=EL\frac{di}{dt}+Ri=E

Rewrite;

Didt+RLI=EL\frac{Di}{dt}+\frac{R}{L}I=\frac EL

The integrating factor;

I.F=eRLdt=eRtLI.F=e^{\int \frac RLdt}=e^{\frac{Rt}{L}}

I put into the equation;

eRTL[didt+RLi]=eRtLELe^{\frac{RT}{L}}[\frac{di}{dt}+\frac RLi]=e^{\frac{Rt}{L}}\frac EL

Integrating respectively;

I=ER+ceRtLI=\frac ER+ce^{\frac{-Rt}{L}}

At t=0,i=0;

c=ERc=-\frac ER

i=EREReRtLi=\frac ER-\frac ERe^{\frac{-Rt}{L}}

Substitute the values;

i=200100200100e100×24i=\frac{200}{100}-\frac{200}{100}e^{\frac{-100×2}{4}}

I=9.837AI=9.837A



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