Current in circuit with many resistors

[miyayeah]

Homework Statement

Find the current and potential difference through 3Ω resistor.

Homework Equations

ε - I₁ (Ω) - I₂ (Ω) ... = 0

The Attempt at a Solution

I only got as far as finding the equation:
ε - I₁ (3Ω) - I₂ (16Ω) = 0 (For complete loop around circuit)
I know I have to find I₁, but I don't know the value of I₂ too, so I'm not sure how I need to start the question.

This is due midnight, any help would be appreciated.

 

[lewando]

Why don't you try simplifying the circuit first. Can you think of what you can do with the other resistors (4Ω, 48Ω, 16Ω)?

 

[BvU]

When you compare the voltages over the 3, 16 and 48 ohm resistors, what do you notice ?
Can you redraw the diagram so it looks more familiar ?

 

[haruspex]

Can you identify some resistors in parallel? Do you know how to calculate the effective resistance of the set?

 

[BvU]

hehe...

 

[miyayeah]

Can you identify some resistors in parallel? Do you know how to calculate the effective resistance of the set?

I believe 4Ω and 48Ω resistors are in parallel.
R_eq = (1/R₁ + 1/R₂ +...) ^-1.
But how would this help solve the problem?

When you compare the voltages over the 3, 16 and 48 ohm resistors, what do you notice ?
Can you redraw the diagram so it looks more familiar ?

I tried drawing it in two different parts, but I'm not sure how to combine the two, if they are right.

 

[lewando]

I believe 4Ω and 48Ω resistors are in parallel.

They are indeed in parallel. Is there another resistor nearby that could also be considered in parallel with the 4Ω and 48Ω?

Req = (1/R1 + 1/R2 +...) -1.
But how would this help solve the problem?

If you can find the R_eq as seen by the voltage source, finding the current becomes easy. And if you know the current going through the 3Ω, finding the voltage across it becomes easy. Recognizing the parallel resistors is the first step.

I tried drawing it in two different parts, but I'm not sure how to combine the two, if they are right.

BvU was asking you to redraw your original circuit so that the parallel resistors would be more obvious. Drawing those two circuits, as you did, is not what he had in mind.