Visualization of resistance

Question

What does a resistor do in an electrical circuit? Does it impede the flow of electrons by increasing offering a path that offers a large no. of collisions? How can i visualise it, i have been told to think of water flowing in a pipe and which has a narrow part like this

the number of water molecules in the broader cross-section is more than the number of water molecules in the narrower cross-section, velocity increases to make sure that amount of water entering=leaving, it appears to me as if(no. of water molecules flowing in a cross-section) /time remains constant. Now in a wire this would imply constant current, so i am confused here. Wait, isn't current constant in seris, so is this true ? Now, no of electrons is more in laeger cross-section than smaller cross-section this means more charge in larger than smaller and more charge means more potential, so is this the reason why we say resistor changes the voltage of circuit ? I know that kinetic energy is reduced due to collisions leading to heat loss.

Answer 1

I have been told to think of water flowing in a pipe and which has a narrow part

I don't think the narrow pipe is a good analogy of a resistor.

In simple fluid dynamics the water in the narrow part of the pipe speeds up so that the flow rate remains constant i.e. $A_1v_1 = A_2v_2$, but there is no loss of energy in the pipe, because the fluid is assumed to flow without friction or viscosity.

However, in a resistor there is a loss of energy because there is a voltage drop across the resistor. A typical resistor is made of a material like finely powdered carbon, which obstructs the flow of electrons through it.

The Wikipedia article on resistors suggests that rather than simply a narrow pipe, a better analogy is a clogged or obstructed pipe, where a higher pressure (which is the analogy of voltage) is required to maintain a given flow rate through the pipe.

Answer 2

What does a resistor do in an electrical circuit?

The resistance of a conductor limits the amount of current that can flow in the conductor for a given potential difference.

I have been told to think of water flowing in a pipe and which has a narrow part like this. Now in a wire this would imply constant current, so i am confused here. Wait, isn't current constant in series, so is this true ?

Yes the current is constant in resistors in series. If it were not, charge would build up.

You need to start with a basic definition of current, such as:

Electric current $i(t)$ through a surface is defined as the rate of charge transport through that surface, or

$$i(t)=\frac{dq(t)}{dt}$$

Where $q(t) denotes instantaneous charge.

Since the two sections of pipe, analogous to two resistors, are in "series", the rate of water flow across the wider section must equal that across the narrower section, lest water (analogous to charge) builds up somewhere.

Now, (the) no of electrons is more in larger cross-section than smaller cross-section

The number of electrons that cross the surface is greater in the larger cross section, but their drift velocity is lower, so that the rate of transport of electrons (current) through both surfaces is the same. For a good microscopic view of electric current, see: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html

...this means more charge in larger than smaller and more charge means more potential, so is this the reason why we say resistor changes the voltage of circuit

I find this a bit confusing. But start with a basic definition of the potential difference ($V$) between two points:

The potential difference $V$ between two points is the work per unit charge required to move the charge between the points.

More work is required per unit charge to move the charge through the same length of the higher resistance resistor (narrow "pipe") than to move the charge through the same length of the lower resistance resistor (wider "pipe"). So the voltage drop per unit length is higher for the narrow section than the wide section.

The water analogy is the pressure difference per unit length of the narrow section of pipe is greater than the pressure difference per unit length of the wider section of pipe. More work per unit mass of water is needed to push the water through a given length of the narrow pipe than for the same length of the wider pipe.

Hope this helps.

Answer 3

As the other answer has pointed, there is not a direct analogy between the two situations but I would like to add that you can force-create an analogy between fluid flow in a pipe and current flow in a circuit with the knowledge of the Poiseuille Equation. Note though that the actual electrodynamics of the flow of electrons is not anything like the flow of water atoms in pipes.

Vaguely speaking, it is the 'flow' of electrons in the wires that is creating an electric current, i.e. the flow rate of charges. This flow can brutely be correlated to the volume flow rate, $Q$ in fluid flow.

Poiseuille Equation states: $Q=\frac{\Delta P \pi r^4}{8\eta l}$ As we have modelled the volume flow rate, $Q$, after charge flow rate, $I$, it seems to come natural that we might correlate $\Delta P$ and $\Delta V$, that are, in both cases, the agents that are driving this flow across the section. Hence, $R=\frac{V}{I}$ matches in its form to $\frac{8\eta l}{\pi r^4}=\frac{\Delta P}{Q}$. Denoting the left hand side by $\rho$, you can see the analogy between circuital resistance and this 'fluid flow resistance'.

• More $l \implies$ more force required to push the fluid,
• More $r \implies$ less hindered flow due to larger cross-section,
• More $\eta$ , i.e. viscosity, $\implies$ analogously means more inter-electronic repulsion and hence a more hindered flow.