- #1
Arshad_Physic
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Series Circuit DIfferential Equation - My answer is coming out to be wrong...
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.
1) L di/dt + Ri = E(t)
or
2) R dq/dt + q/C = E(t)
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
=> Ee0.83333 - (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!
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
=> Ee0.83333 - (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!