Series Circuit DIfferential Equation - My answer is coming out to be wrong

[Arshad_Physic]

Series Circuit DIfferential Equation - My answer is coming out to be wrong...

Homework Statement

A 6.5 amp current is necessary in order to start the motor for a certain factory appliance. The circuit for the appliance is designed with a 2 ohm resistor and a 1.5 henry inductor. If there already exists a steady current of 2 amps in the circuit at time t = 0, what electromotive force is necessary to achieve the desired current in 1.25 seconds?

The answer should be 15.1 volts.

Homework Equations

1) L di/dt + Ri = E(t)

or

2) R dq/dt + q/C = E(t)

The Attempt at a Solution

It makes sense to me to use Equation (1):

L di/dt + Ri = E(t)

1.5 di/dt + 2i = E(t)

=> di/dt = [E(t) - 2i ] /1.5

=> di/[E(t) - 2i] = dt/1.5

=> ln[E(t) - 2i) = t/1.5 + c

=> E(t) = Ae^-t/1.5 + 2i

i(o) = 2

A = E - 4

=> E(t) = (E-4)e^-t/1.5 + 2i

i(1.25) = 6.5

=> E(t) = (E-4)e^-1.25/1.5 + 13

=> E - (E-4)e^-0.83333 = 13

=> Ee^0.83333 - (E-4) = 13e^-0.83333

=> Ee^-0.83333 - E + 4 = 29.9126

=> E(e^-0.83333 - 1) = 25.9126

=> E = 19.9178 Ans.

The answer should be 15.1 volts. PLease help! What is the thing that I am doing wrong!

Thanks!

 

[andylu224]

First off, Your entire method could not possibly work if E(t) is not simply a constant, but thankfully in this case it is. You only made one simple mistake when you integrated di/[E-2i]. you're missing a -1/2 in front of the ln|E-2i|.