Rate of change of current in an R-L Circuit

In summary, the conversation discusses the concept of current changing through an inductor and under what conditions this change can occur. The group discusses the use of source transformation and Laplace to arrive at the correct answer, and also clarifies the role of impulse voltage sources in this scenario. Ultimately, the conversation concludes that the current across an inductor cannot change suddenly unless the input is an impulse voltage source.
  • #1
jaus tail
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Homework Statement


upload_2018-5-18_12-18-4.png


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.
 

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  • #2
jaus tail said:
Book has mentioned answer as B which is weird cause there is no Ls in circuit.
It's probably a typo. They meant Is instead of Ls.

jaus tail said:
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.
 
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  • #3
Wow... I used laplace and then got the answer. You're right.
upload_2018-5-18_16-41-37.png

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.
 

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  • #4
jaus tail said:
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 Rtotal=Rs+R and inductance L, excited by a voltage source of emf IsRs.
At t=0+, no current flows through the inductor, which means the entire source voltage appears across the inductor.
So, IsRs=Ldi/dt, which gives di/dt=IsRs/L.
jaus tail said:
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 VL 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.
 
  • #5
Well you're method is way quicker than mine.
Thanks a lot. Learnt new thing today.
 

1. What is the formula for calculating the rate of change of current in an R-L circuit?

The formula for calculating the rate of change of current in an R-L circuit is dI/dt = -R/L * I, where dI/dt represents the rate of change of current, R is the resistance of the circuit, L is the inductance of the circuit, and I is the current flowing through the circuit.

2. How does the resistance affect the rate of change of current in an R-L circuit?

The resistance in an R-L circuit affects the rate of change of current by slowing down the flow of current through the circuit. This is because the higher the resistance, the greater the opposition to the flow of current, resulting in a slower rate of change of current.

3. What is the role of inductance in the rate of change of current in an R-L circuit?

Inductance plays a crucial role in the rate of change of current in an R-L circuit. It is the property of a circuit that causes a counter-EMF (electromotive force) to be induced when the current in the circuit changes. This counter-EMF opposes the change in current, resulting in a slower rate of change of current.

4. How does the initial current affect the rate of change of current in an R-L circuit?

The initial current in an R-L circuit affects the rate of change of current by determining the starting point of the current change. The initial current sets the initial conditions for the circuit, and the rate of change is calculated from that point on.

5. Can the rate of change of current in an R-L circuit be negative?

Yes, the rate of change of current in an R-L circuit can be negative. This happens when the current is decreasing over time, resulting in a negative value for dI/dt. It is important to keep track of the sign of the rate of change to understand the direction of current flow in the circuit.

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