Voltage and Current in a Combination Circuit

[scowl]

Homework Statement

All the batteries shown are 1 V.

What voltage is supplied by the batteries in this circuit?

What is the current through the branch of the circuit containing the 20 Ω resistor?

What is the current through the branch of the circuit containing the 30 Ω resistor?

What is the total current of the circuit?

What is the total resistance of the circuit?

Homework Equations

Voltage (V) = Current (I) / Resistance (R)

I_branch = V_total / R_branch

I_total = I_{branch 1} + I_{branch 2} + ...

R_total = V_total / I _total

The Attempt at a Solution

The problem is that I can't determine the effect of this arrangement of batteries. If the batteries were replaced with a single battery of, say, 3 V (or a series with this as the total), then the current through the 20 Ω resistor would be .15 A and the current through the 30 Ω resistor would be .1 A, the total current would be .25 A, resulting in the total resistance being 12 Ω.

However, with this battery arrangement, I can't determine if it would act as a series circuit with 3V or a parallel circuit with 2V. Additionally, I'm not sure what effect a parallel arrangement would have on the current of the entire circuit.

 

[phinds]

How do you determine series vs parallel and how does that apply to the battery arrangement?

 

[scowl]

Series would be the batteries arranged end to end like this.

The result would be that the voltage would be cumulative of the batteries in the series.

Parallel would be the batteries arranged like this.

The result would be that the voltage would be equal to that of a single battery (provided they all have the same voltage, which if they didn't would be another issue). However, the current would be cumulative.

So, given that the battery arrangement is two batteries in parallel acting as the first cell of a series, the voltage should be 2 V. However, all other examples I've seen of this arrangement had the second cell consisting of two batteries in parallel as well. Does this mean that the batteries in this problem will only have the current of a single battery?

 

[Doc Al]

Are you familiar with Kirchhoff's laws?

 

[phinds]

Parallel would be the batteries arranged like this. Does this mean that the batteries in this problem will only have the current of a single battery?

current is not a matter of series or parallel, it is a matter of Ohm's Law.

 

[NascentOxygen]

Does this mean that the batteries in this problem will only have the current of a single battery?

You can imagine each of the two parallel cells contributing just half of the total current (this assumes they are perfectly identical in all respects). The single cell they connect to must carry the full current because it has no parallel twin to share with.