Answer to Question #306159 in Differential Equations for Rex

Question

An inductance of 1 henry and a resistance of 1 ohm are connected in series with a constant e.m.f. of E volts. If 10 A after 5 seconds, find E

Answer 1

$$I(t)=\frac{\cal E}{R}\left(1-e^{-Rt/L}\right)$$

$${\cal E}=\frac{I(t)R}{\left(1-e^{-Rt/L}\right)}$$

$${\cal E}=\frac{10*1}{\left(1-e^{-1*5/1}\right)}=10.07\:\rm V$$