Question #305647

An inductance of 1 henry and a resistance of 1 ohm are connected in series with a constant EMF of E volts. If the current is initially zero, and is equal to 10 A after 5 seconds, find E.


1
Expert's answer
2022-03-07T17:20:04-0500

LdIdt+RI=EL\frac{dI}{dt}+RI=E

1dIdt+1I=E1\frac{dI}{dt}+1I=E

dIdt+I=E\frac{dI}{dt}+I=E

dIdt=EI\frac{dI}{dt}=E-I

dIEI=dt\frac{dI}{E-I}=dt

integrate both sides;

dIEI=dt\int \frac{dI}{E-I}=\int dt

log(EI)0i=t0t-log(E-I)|_0^i=t|_0^t

at t=5, I=10A

Replace the above conditions in the integral;

log(E10)=5-log(E-10)=5

logE10=5log\frac{E}{10}=-5

E10=e5\frac{E}{10}=e^{-5}

E=e510E=e^{-5}*10

E=0.0674VE=0.0674V


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