# Math Help - AC circuit intergration by parts equation

1. ## AC circuit intergration by parts equation

Could any body help i have been trying to solve the solution to an equation for my maths assignment but doesnt match the given final solution that i have. The equation is:

Given that L di/dt + Ri = Esin wt and that i=0 when t=0 show that the solution of the equation is given by

i= [E / R^2 + w^2 L^2](Rsin wt - wL cos wt)+ [ E w L/R^2+w^2 L^2] e ^-Rt/L

Can any body help me???

2. Originally Posted by sarnekat
Could any body help i have been trying to solve the solution to an equation for my maths assignment but doesnt match the given final solution that i have. The equation is:

Given that L di/dt + Ri = Esin wt and that i=0 when t=0 show that the solution of the equation is given by

i= [E / R^2 + w^2 L^2](Rsin wt - wL cos wt)+ [ E w L/R^2+w^2 L^2] e ^-Rt/L

Can any body help me???
Since it's a show question, two approaches are available to you:

1. Substitute the given solution into the differential equation and show that equality is obtained,

or

2. Solve the differential equation $\frac{d i}{dt} + \frac{R}{L} i = \frac{E}{L} \sin (\omega t)$. You could use the integrating factor method here.

Please show what you've done and where you get stuck.