# Finding current for each resistor at different times

## Homework Statement

For the circuit given that R1=10 W, R2=20 W, R3=30 W and L=30 mH, determine the current through each resistor

a) at the moment the switch is closed
b) a long time after the switch is closed

After the switch has been closed a long time it is reopened, determine the current through each resistor

c) at the instant the switch is opened
d) a long time after the switch is opened
e) after the switch is opened, what is the time constant for the circuit?

V=IR

## The Attempt at a Solution

First of all, is it a mistake that the R1,R2, and R3 are in watts, not ohms?
I have not figured out how to solve any of this! Any help is appreciated.

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gneill
Mentor

## Homework Statement

For the circuit given that R1=10 W, R2=20 W, R3=30 W and L=30 mH, determine the current through each resistor

a) at the moment the switch is closed
b) a long time after the switch is closed

After the switch has been closed a long time it is reopened, determine the current through each resistor

c) at the instant the switch is opened
d) a long time after the switch is opened
e) after the switch is opened, what is the time constant for the circuit?

V=IR

## The Attempt at a Solution

First of all, is it a mistake that the R1,R2, and R3 are in watts, not ohms?
I have not figured out how to solve any of this! Any help is appreciated.

The "W's" are probably a typo. In a math font the W's would be rendered as the greek Ω.

You'll need to make a bit more of an attempt to solve the problem before help can be offered. What do you know about the behavior of inductors when sudden changes in the circuit occur? What formula provides the time constant for an RL circuit?

For part a, the inductor will have very high resistance so no current will flow through R3. The current of R1 and R2 will be I1=I2=ε/30Ω.
[/quote]
Yes, that's right.

Is the ε supposed to be given? I don't know how to find voltage with just resistance and inductance.
If the value for ε is not supplied in the problem statement then you'll have to answer symbolically (with a formula that includes ε as you did above).

For part b, the inductor will have no resistance so R3 parallel to R2.
Req=10+(1/20+1/30)-1=22Ω
I1=ε/22
Okay so far.

I2=ε/20
I3=ε/30
Nope. The full value of ε does not appear across resistors R2 and R3; there must be a voltage drop across R1 when current I1 flows though it.

I don't know how to start parts c,d,e.
Well, what property does an inductor have regarding current when a sudden change occurs in the circuit?

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NascentOxygen
Staff Emeritus

## Homework Statement

For the circuit given that R1=10 W, R2=20 W, R3=30 W and L=30 mH, determine the current through each resistor
Resistors' values would usually be in ohms. If your problem sheet is handwritten perhaps each is meant to be an inverted capital Omega, but carelessly drawn and instead resembles a "W"? The inverted Ω is pronounced "mho" and is an older symbol for conductance, $\mho$. It has these days been replaced by "S" for siemens.

Nope. The full value of ε does not appear across resistors R2 and R3; there must be a voltage drop across R1 when current I1 flows though it.

So if I1=ε/22 then V1=(ε/22)R1 and V2=V3=ε-(ε/22)R1
I2=[(ε-(ε/22)R1]/R2 I3=[(ε-(ε/22)R1)]/R3

For part c, I know that inductor has maximum current through it right after switch opens then current slowly decreases to zero with equation Ifinal=Iinitial*e-t/τ. So I guess the currents will be same as in part b for c).

And for d), I don't think there will be any current in the resistors at all.

For e) what do they mean by time constant. Do I solve for tau?

gneill
Mentor
So if I1=ε/22 then V1=(ε/22)R1 and V2=V3=ε-(ε/22)R1
I2=[(ε-(ε/22)R1]/R2 I3=[(ε-(ε/22)R1)]/R3

For part c, I know that inductor has maximum current through it right after switch opens then current slowly decreases to zero with equation Ifinal=Iinitial*e-t/τ. So I guess the currents will be same as in part b for c).
In the case of (c) the switch is open so what current can flow through R1? So what is the available path for the inductor's current?

Now, and this is important, the diagram defines the individual currents and how to interpret their directions (the arrows). Be sure to check the current directions for part (c) !

And for d), I don't think there will be any current in the resistors at all.
Yes. Can you state why that would be?

For e) what do they mean by time constant. Do I solve for tau?
Yes.