What is current across 5 ohm resistor

1. Nov 18, 2016

jaus tail

1. The problem statement, all variables and given/known data
Find the current across 5 ohm resistor

2. Relevant equations
Superposition theorem. Other voltage sources become short circuit and current sources become open circuit.
Ohm's law. I = V / R

3. The attempt at a solution

Using superposition theorem, we get:
When only left side 10 V source is there, is short circuit across right side 10 V source, so current through 5 ohm resistor is zero.
It's the same when only right side 10 V source is acting.
So total current across 5 ohm resistor is zero.

Book says: we cannot have voltage sources of different magnitude in parallel and that current cannot be determined.
For voltage sources of same magnitude in parallel, take only one voltage source and apply ohm's law.

I'm confused. Why should we ignore other voltage source?

Isn't parallel operation of transformer same as above case? Like the load sees two voltage sources in parallel?

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2. Nov 19, 2016

oz93666

The top circuit is imaginary because the two voltage sources are not shown with an internal resistance ..... all batteries have internal resistance which will limit the amount of current they can deliver ,In the circuit one battery is irrelevant .....it would not be in real life because of internal resistance 2 sources would deliver more current to the 5 ohm resister

It's similar in the parallel transformer if only A was used , at high currents the coils could overheat and burn out , having A and B allows double the current to the load , before the transformer gets too hot for comfort.

3. Nov 19, 2016

Staff: Mentor

That's true. BUT in the DC circuit you have drawn the sources are not different. Two identical ideal sources in parallel are no different to one ideal voltage source of identical voltage. So you can analyse the circuit with just one 10V source.

⏩ BTW, I'm left wondering did you intend to show one source with polarity opposite to that of the other? Otherwise, in the circuit as drawn I don't see a problem.

If you connect a +10.000V source between points in a circuit which are already at a potential difference of +10.000V then nothing happens, nothing changes. No current will flow to or from that source.

4. Nov 20, 2016

jaus tail

Thanks. There are actually three problems in book. One with two voltage sources of same polarity and different magnitude in parallel, second problem has 2 voltage sources of same polarity and magnitude in parallel, and third problem has two sources of same magnitude but opposite polarity in parallel.