Originally Posted by **JollyJohn** Hi, I'm hoping someone would be able to help me with this question. I'm struggling with the mathematics of this question. I'm not sure quite how to go about it. *The circuit current (i) in an electrical circuit containing resistance (R) and inductance (L) in series with a constant voltage source (E) is given by the differential equation ***E-L(di/dt)=Ri** (t being time).
Solve the equation and find the circuit current (i) in terms of time (t), given that when t=0, i=0 (boundary condition).
The following are known:
E=VR+VL
VR=iR
VL=L di/dt
E=iR+Ldi/dt
Solution parameters input;
E=1
R=1
L=1
t=0 – 10 s with interval of 0.01s (range for solution) |

You have the differential equation: L i'+ R i = E, where L, R, E are constants and i' is the time derivative of i. This is a first order linear differential equation for i(t). There are various ways to solve this, the most popular likely being the use of an

integrating factor.

Give it a try and let us know if you need more help.

-Dan