Rate of change of current in an R-L Circuit

[jaus tail]

Homework Statement

Homework Equations

Current cannot change suddenly through inductor unless input is impulse voltage source.

The Attempt at a Solution

since input is DC source we have i(0+) = i(0-) so we have di/dt at t = 0+ is 0.
Is it correct? Book has mentioned answer as B which is weird cause there is no Ls in circuit.

 

[cnh1995]

Book has mentioned answer as B which is weird cause there is no Ls in circuit.

It's probably a typo. They meant I_s instead of L_s.

since input is DC source we have i(0+) = i(0-) so we have di/dt at t = 0+ is 0.

No.
How about using source transformation? It will make the circuit look more familiar.

 

[jaus tail]

Wow... I used laplace and then got the answer. You're right.

But shouldn't it be zero as per concept? Unless the input is an impulse voltage source the current across inductor cannot change so quickly. V = L di/dt. So unless V is an impulse, di/dt has to be zero.

 

[cnh1995]

Wow... I used laplace and then got the answer. You're right.

Well, if you use source transformation, you end up with a series RL circuit with R_total=R_s+R and inductance L, excited by a voltage source of emf I_sR_s.
At t=0⁺, no current flows through the inductor, which means the entire source voltage appears across the inductor.
So, I_sR_s=Ldi/dt, which gives di/dt=I_sR_s/L.

the current across inductor cannot change so quickly. V = L di/dt. So unless V is an impulse, di/dt has to be zero.

No, here V_L at t=0 is not zero, hence di/dt is also not zero. You can't compare the currents at t=0^- and t=0⁺ to find di/dt at t=0⁺ because at t=0^-, the inductor was not excited.

 

[jaus tail]

Well you're method is way quicker than mine.
Thanks a lot. Learnt new thing today.