How Do You Calculate Currents Through Multiple Resistors in a Circuit?

[YamiBustamante]

Homework Statement

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Use the following values: E = 12.0 V , R1 = 35.0 Ω , R2 = 22.0 Ω , R3 = 41.0 Ω , and R4 = 14.0 Ω .

Find the following currents:

• the current I1 through the resistor of resistance R1 = 35.0 Ω
• the current I2 through the resistor of resistance R2 = 22.0 Ω
• the current I3 through the resistor of resistance R3 = 41.0 Ω
• the current I4 through the resistor of resistance R4 = 14.0 Ω

Homework Equations

ε - RI = ΔV
I = ε/R
R being the resistance
I being the current

The Attempt at a Solution

So from what I understand I_3 = I_4 and I_2 = I_2 + I_3 (or I_4 since they're equal)
Not sure if my math is correct.

I tried using I = ε/R for all of them.
For
I_1 = 0.343
And,
1_3 (or 1_4) = 12/(41+14) = 0.218
Finally,
1_2 = 0.218 + 0.218 = 0.436

Tried using ε - RI = ΔV and I got the same answer for I_1 and I_3/I_4, but I get different answers I_2.
Is my math wrong?

 

[cnh1995]

Are you familiar with KVL?

 

[andrewkirk]

I tried using I = ε/R for all of them.
For
I_1 = 0.343

You got that by dividing 12V by 35 ohms. That's not correct, because the formula only works when the resistance is measured over the same part of the circuit as the Potential Diff. You've used the total PD between the terminals but only used the resistance for R1, which is only a small part of the circuit between the terminals.

Do you know how to work out the resistance of parallel wires?
If so, first work out the resistance Rp of the set of wires that is R1 in parallel to (R3+R4).
Then work out the resistance Rtot of R2 in series with Rp.
Then you can work out the total current from E and Rtot.
Then work backwards to allocate the current between resistors.