In Problem 24, find a system of differential equations and initial conditions fo

Question

In Problem 24, find a system of differential equations and initial conditions for the currents in the networks given by the schematic diagrams; the initial currents are all assumed to be zero. Solve for the currents in each branch of the network.

Please be thorough with your work and give the correct answer. That is what I am looking for. Thank you!

In Problem 24, find a system of differential equations and initial conditions for the currents in the networks given by the schematic diagrams; the initial currents are all assumed to be zero. Solve for the currents in each branch of the network.

Explanation / Answer

differential eq's are

L*dI1/dt + 10*I2 = 50 ( L= 0.005 H )

L*dI1/dt + 2L*dI3/dt + 20*I3 = 50

2L*dI3/dt + 20*I3 = 10*I2

and intial currents are zero

so I1(0+)=0,

I2(0+)=0,

I3(0+)=0

I'1(0+)=50*L

form above eq's wc can get I1, I2, I3

I1 = 7.5 - 6.66*(e^-1000t) - 0.833*(e^-4000t)

I2 = 5.0 - 1.25*(e^-4000t)

I3 = 2.5 - 6.66*(e^-1000t) + 0.416*(e^-4000t)

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