Energy Conservation in Parallel Circuits

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So each “closed loop” experiences the same voltage drop as the emf of the cell. So if you added the “total” voltage drop in the circuit, it would exceed that provided by the cell.

Voltage is Joules per Coulomb.

The number of Coulombs in a circuit is fixed.

Maybe it is the product of Voltage and Current which is conserved in parallel circuits? I’m struggling to work it all out in my head probably because I’m not sure what the basic rules of circuits are and how they relate to Physics I’ve encountered elsewhere. It all just seems a little bizarre and contradictory.

(UK A-Level)

In: Physics

>So if you added the “total” voltage drop in the circuit, it would exceed that provided by the cell.

It would, which is why this is wrong to do. You only add voltages which are in series. You should do a refresher on Kirchhoff’s laws before you proceed any further down your electrical courses.

>Voltage is Joules per Coulomb.

>The number of Coulombs in a circuit is fixed.

These two ideas are a terrible way of approaching it. Volts should be treated as a fundamental unit in electricity.

>Maybe it is the product of Voltage and Current which is conserved in parallel circuits?

**THIS** is finally correct. The energy coming out of your voltage source is equal to the voltage times the current through branch one plus the voltage times the current through branch two. This is the same as the voltage of the source times the current leaving the source. The same voltage is applied across each branch, but the current from the source splits between them.

There are major flaws in your intuition.

If you are at A level, I assume you know that work done = force x distance.

Imagine you have a road between your house and school that is 1km long. One day you decide that a new road is needed and you build a second road parallel to the existing road. Since now you have 2 roads each 1km long, could you say you’ve violated energy conservation because now you have a total of 2km of road rather than 1?

Say you have a sibling that both travel to school. And rather than each of you taking the same road, one of you use the old road and the other the new road. Did you double the amount of work needed in total for the both of you to get to school once each of you took a different road? (assume that the force needed per person is the same)

Using your own analogy, if you have a fixed number of coulombs but had 2 paths, you’d divide the coulombs across the 2 paths. So the total energy content remains the same since it (in total) it is the same number of coulombs travelling across the same voltage, they just took different paths. [this is a very bad analogy for future intuition, by the way]

A more commonly used analogy (that gives a better intuition) is to think of your circuit as water pipes, voltage is the pressure difference and current is the flow rate of the water in the circuit.

>The number of Coulombs in a circuit is fixed.

No, the current (coulombs/sec) in a series circuit is equal everywhere in the loop. It is not necessarily fixed.

In a series circuit every device gets the same current, but has a voltage which depends on its resistance.

In a parallel circuit every device gets the same voltage, but has a current which depends on its resistance