Can someone please tell me if my logic is right regarding the above circuit? I'm trying to find the voltage, v for t > 0

i(t) = i(inf) + (i(0) - i(inf))*exp(-t/(R/L))

At i(0), the current across the 10ohm resistor will be 2 A as the inductor causes the current in its branch to be zero -> current can't change instantaneously.
At t(inf), the inductor will be short circuit to steady state dc, so circuit acts like a current divider and the current across the resistor in question will be

Ix = (Rt/Rx)*(Is) = (5/10)*2 = 1.

so the current flowing throug the resistor in question for t > 0 will be

i(t) = 1 + (2 - 1)*exp(-t/20) = 1 + 1*exp(-t/20)

thus the voltage will be 10 + 10*exp(-t/20)

answer says i'm right, but when i showed my working to my tutor, he didn't know what the hell i was on about.

 

Vanush,

i(t) = i(inf) + (i(0) - i(inf))*exp(-t/(R/L))

You defined the current source as 2u(t), which means constant 2 amps after t>0. Why do you show it as variable with time?

At i(0), the current across the 10ohm resistor will be 2 A as the inductor causes the current in its branch to be zero -> current can't change instantaneously.

Current cannot change instantaneously in the coil, you mean. That value of zero is only true at the t=0 instant.

answer says i'm right, but when i showed my working to my tutor, he didn't know what the hell i was on about.

Yes, your logic is correct, but you probably need to learn a systematic method of calculation for loop circuits like these in order to solve more complicated problems that are not so intuitive. Ratch

 

Vanush,



You defined the current source as 2u(t), which means constant 2 amps after t>0. Why do you show it as variable with time?

I mean the current flowing through the 10 ohm resistor that i want to know the voltage of