# Can the the rate of the flow of electrons (current) remain the same even though the number of coulombs differ?

I understand the concept of a current, and how current is defined by the amount of coulombs passing through a point in the circuit, per second.

What I'm confused about is when it comes to parallel circuits, and how currents are not constant.

If current is the rate of which charge flows, do speeds of the electrons matter on how many they are. For example, can't a group of 0.5 coulombs of charge flow as fast a 1 coulomb of charge? Why is current dependent on the number of coulombs? It's kinda like a drop of water running down a pipe as fast as a stream of water. So what really is current....?

And since voltage is proportional to current, does that mean it is also proportional to charge (amount of coulombs). So a higher value of coulombs will result in a higher value of voltage...?

Apologies in advance if I sound like a neanderthal.

• To grasp these ideas you are expressing, it would be easier for you to think of charge as a volumetric integral of charge density. If you have some calculus understanding, check this: en.wikipedia.org/wiki/Charge_density. This charge density times charge speed equals current density, and then current will be its integral in the cross-section surface of the conductor. I know that I've just spilled too much formal jargon, but sometimes the only way to truly understand something is to let go of associations like "water stream". – Vicente Cunha May 18 '18 at 11:58
• I'm having trouble formulating an answer because it is not clear to me where your doubt is. How do you arrive at the point that currents in parallel circuits are not constant? I'm also unsure if I understood your second point correctly. Are you asking if a charge of 0.5 C could create the same current as a charge of 1 C? – Arsenal May 18 '18 at 12:27
• Current is not dependent on the number of electrons, but on the number of electrons flowing per second. – Chu May 18 '18 at 13:17

If current is the rate of which charge flows, do speeds of the electrons matter on how many they are.

Does the speed of 50 cars driving down a road affect the number of cars passing down the road?

For example, can't a group of 0.5 coulombs of charge flow as fast a 1 coulomb of charge?

Electrons have a varying speed but it's the number of electrons that pass per second that dictates current.

Why is current dependent on the number of coulombs?

Because current IS the rate of change of charge, dQ/dt

It's kinda like a drop of water running down a pipe as fast as a stream of water. So what really is current....?

It's the rate of change of charge, dQ/dt

And since voltage is proportional to current, does that mean it is also proportional to charge

I hear the sound of a can of worms being opened....

Energy (W) = $\dfrac{CV^2}{2}$ for a capacitor But we also know that Q=CV therefore we can re-write the energy equation as: -

$$W = \dfrac{CQ^2}{2C^2}$$

If we then differentiate to find rate of change of energy with respect to charge we get: -

$$\dfrac{dW}{dQ} = \dfrac{Q}{C}=V$$

Voltage is much harder to put your finger on but in words.....

It's the rate of change of energy with respect to charge


Just as the velocity of a moving mass....

Is the rate of change of energy with respect to momentum