Circuit Question Involving Resistors and Inductors

[Jordan1361]

Homework Statement

For the circuit below, if L=2.0 H, emf=10 V, R1=10 ohms, R2= 20 ohms, what is the current through each component

a) at the instant the switch is closed
b)a long time after the switch is closed
c) If after a long time the switch is reopened, what is the time constant for the current?

Homework Equations

V=IR

The Attempt at a Solution

For a) I think the resistors are in series so equivalent resistance would be 30 ohms. Then I used V=IR to find a current of 0.33 A.

Could someone please check if a) is right and show me the steps to do the other parts. Thanks!

 

[berkeman]

Homework Statement

For the circuit below, if L=2.0 H, emf=10 V, R1=10 ohms, R2= 20 ohms, what is the current through each component

a) at the instant the switch is closed
b)a long time after the switch is closed
c) If after a long time the switch is reopened, what is the time constant for the current?

Homework Equations

V=IR

The Attempt at a Solution

For a) I think the resistors are in series so equivalent resistance would be 30 ohms. Then I used V=IR to find a current of 0.33 A.

Could someone please check if a) is right and show me the steps to do the other parts. Thanks!

The current you calculated for right after the switch is closed is correct. What about the current a long time after the switch is closed? What is an inductor's impedance at DC?

 

[Jordan1361]

After a long time, the inductor will act like a piece of wire with no resistance so current would still be flowing through R1 but zero current would be in R2. The current in R1 would be I=10/10=1 A. Am I correct?

For part c, I know that the time constant is tau=L/R so do I just use L=2.0 H and R=0 ohms?

 

[berkeman]

After a long time, the inductor will act like a piece of wire with no resistance so current would still be flowing through R1 but zero current would be in R2. The current in R1 would be I=10/10=1 A. Am I correct?

Yes, very good.

For part c, I know that the time constant is tau=L/R so do I just use L=2.0 H and R=0 ohms?

When the switch is opened, what is in parallel with the inductor? The inductor current cannot change instantly, so it will decay with what time constant?

 

[Jordan1361]

R2 is in parallel with the inductor. I know that current decrease is represented by
I(final)=I(initial)*e^(-t/τ).

 

[berkeman]

R2 is in parallel with the inductor. I know that current decrease is represented by
I(final)=I(initial)*e^(-t/τ).

Looks good!

 

[Jordan1361]

So the time constant is τ=-t/ln(I_final/I_initial)
There is no value for part c?