Find the current in electric circuit is given by L di/dt+iR = E Where E= 6 volts, R=100 ohms L = 0.1 Henry and how long will be it before the current has reached one-half its maximum value.
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Answer:
Let I be current at ant time t
EMF E=5 volts , resistance R=50 ohms and inductance L=1 henry
The basic equation of current for RL circuit is
dt
dI
+
L
R
I=
L
E
⇒
dt
dI
+50I=5
This is a linear equation and the solution of it is I=ce
−50t
+
10
1
At t=0 , I=0. So we get c=−
10
1
Therefore the equation for current will become I=−
10
1
e
−50t
+
10
1
As t tends to infinite , the value of I tends to
10
1
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