Why voltage is same across parallel resistance?

Since voltage stands for energy per unit charge to be used to carry it from one point to another,why should energy per unit charge be same for two resistors of different resistances,?the energy required would be more in the resistor with high resistance. Where did I go wrong?

• i think where you went wrong is thinking about the power. Ignore the resistors, amperage etc. You have 2 or more parallel branches. If you hook a 9v battery to it, you simply supply 9v to each branch irregardless of what resistors are there. Your voltage is just potential energy, nothing more.
– Rick
Commented Aug 30, 2020 at 15:20

A heuristic approach that might complement the more deeply based explanations...

Imagine connecting a voltmeter across one of the resistors. Then we decide to measure the voltage across the other one. But we don't have to change where we connect the voltmeter, because the resistors are connected together in parallel by wires of negligible resistance. So there is no distinction between the voltage across the first resistor and the voltage across the second: the voltages are one and the same!

There is direct analogy with measuring the height differences between the top and bottom of a staircase and the top and bottom of a ramp, when the staircase and the ramp both connect the same two floors of a building. In this case the height difference measures the gravitational potential difference between the two floors.

From Ohm's law, V=IR. The potential V across both resistors in parallel is equal, but there is less current I=q/t in the resistor with greater R. That is, there is less charge moving in a given time; so the energy per charge remains the same. This is the meaning of Ohm's law.

Voltage is the electric potential difference.

An electric potential is electric potential energy supplied by the battery per unit charge.

Note that electric potential is per unit charge, whereas electric potential energy is the exact value of energy for whatever amount of charge you want.

That means, every single electron gets the same electric potential energy.

Even though electrons diverge in a parallel circuit, electric potential energy supplied to each electron does not change. Therefore, the electric potential difference (=voltage) is same.

Or you can think this way.

You feed 100 runners, providing a 500 g steak for each one. Even though at some time you split them to run in differnet roads, in whatever ratio of runners, runners at both roads can only produce the energy worth of a 500 g steak.

If you have two wires connected in parallel, and one wire is connected to a higher resistance than the other. Then, in the wire with the higher resistance the current flowing will be smaller, which compensates the higher resistance and hence keeping the voltage equal, since $$V = iR$$.

Imagine the simplest circuit of two resistances in parallel:

When we consider ideal wires, one property you find is that the whole section of wire is at the same potential. No matter how big it is, the whole wire is at the same potential.

What potential is it? In this case, the ones provided by the battery. Let's consider the blue part to be $$0V$$. The red part is the voltage of the battery.

So, if you look at the resistances, there is the same difference between both terminals.

This is a consequence of the wires having the same potential everywhere. In particular, both branches have the same potential in each side.

If the voltage is the same at the beginnings, and it is the same at the ends... the poetntial difference must be the same.

• Getting the OP to draw a diagram may help them understand...
– user207455
Commented Jul 15, 2019 at 10:52
• Okay. I didn't have much time before, but now I will. Thanks Commented Jul 15, 2019 at 13:14
• yes the voltage between points A and B is the same (the resistance of the wires separating those points is Zero) Commented Sep 5, 2020 at 15:34