# Resistance & Electrical Circuits

• Jimmy87
In summary: So resistivity is the shape of the bars!Now, if we have a circuit made of these bars, the current through each one of them will be proportional to the voltage across them, because the current is the product of the voltage and the flow of charge.But what we're really interested in is the power dissipation in the circuit. And the power dissipation in a circuit is the product of the current and the voltage, so you can rewrite the equation to get P=I²R.In summary, resistors dissipate energy by limiting the current flow through them.
Jimmy87
Hi, I am massively confused with what resistance is and how it applies to circuits and would be very grateful if someone could help. I know this sounds like a basic question but I have been reading for hours and the more I read the less it makes sense. My book says that resistance is 'the property of a material which makes moving charges dissipate their energy'. It talks about the electrons in a wire interacting with the atomic lattice of the material resulting in electrons transferring their energy to the lattice.

If you now consider two very simple circuits each of which has the same source voltage of 6V; one has a 10 ohm resistor and the other has a 30 ohm resistor. According to my book the 30 ohm resistor has a greater tendency to dissipate the energy of the charges. However, the voltage drop across each resistor is the same (6V) therefore each coulomb of charge will dissipate 6J of energy. So if each unit of charge has no choice except to dissipate 6J of energy then how can this be a definition of resistance as each unit of charge is dissipating the same amount of energy? My book also says electrons gain kinetic energy from voltage source and transfer this energy by colliding with the lattice. But wouldn't this mean that when the electrons pass the resistor they would have zero kinetic energy?

Finally, I know that the current in the circuit with the 30 ohm resistor will be less but what causes this specifically as I don't see how you can explain the slowing down of current AND the transfer of energy with the same information - i.e. interactions with the atomic lattice.

Any help is much appreciated!

Resistance is not that complicated, but your book seems to be doing a bad job of it.

Some materials, known as resistors, have the property where the amount of current through the material is proportional to the voltage across the material. Resistance is simply the constant of proportionality between voltage and current: V=IR. That is it.

I would take the above as the definition of resistance. From that definition you can easily derive the fact that resistors dissipate energy, but I would not take the dissipation of energy as the definition. I would take the proportionality between voltage and current as the definition of resistance.

To show the relationship between energy dissipation and resistance simply note that the power dissipated is the product of the current and the voltage, so P=IV. Then substitute in the definition of a resistance to get P=I²R=V²/R. Note that R can appear on the top or the bottom of the power dissipation equation depending on whether the current or the voltage is fixed, so using energy dissipation as the definition is problematic at best.

1 person
Note that the power dissipation of a resistor is given off as heat, and is measured in terms of watts.

You can compare the current through your 30Ω and 10Ω resistors to water flowing from a single pipe that branches into two pipes, one of which is narrower (the 30Ω one) than the other. Naturally, there is more current through the wider pipe. "Resistance" should therefore be interpreted literally.

Not sure if this is helping, maybe not.

maybe think of it like this. You know voltage is the measure of energy (joules) per unit charge (coulombs). Amperes is a measure of charge (coulombs) per unit time (seconds). The product of the two gives Joules per second, or watts (power dissipation). In the 10 ohm circuit, the resistor limits the current flow to 6/10 amps and in doing so, drops the entire 6 volts. It took 6/10 amps to drop it. in the 30 ohm circuit, LESS current (6/30) drops the entire voltage. It means that charge is more susceptible to losing the energy it carries when moving through a higher resistance.

Make any sense?

1 person
Jimmy87 said:
Hi, I am massively confused with what resistance is and how it applies to circuits and would be very grateful if someone could help. I know this sounds like a basic question but I have been reading for hours and the more I read the less it makes sense. My book says that resistance is 'the property of a material which makes moving charges dissipate their energy'. It talks about the electrons in a wire interacting with the atomic lattice of the material resulting in electrons transferring their energy to the lattice.
That's resistivity. Property of a material which makes moving charges dissipate their energy is known as resistivity.

Let's say we have a big slab of some material with some resistivity. If we cut some bar shaped objects out of that slab, those bars will have some resistance, which depends on the resistivity of the material and the dimensions of the bars.

FOIWATER said:
Not sure if this is helping, maybe not.

maybe think of it like this. You know voltage is the measure of energy (joules) per unit charge (coulombs). Amperes is a measure of charge (coulombs) per unit time (seconds). The product of the two gives Joules per second, or watts (power dissipation). In the 10 ohm circuit, the resistor limits the current flow to 6/10 amps and in doing so, drops the entire 6 volts. It took 6/10 amps to drop it. in the 30 ohm circuit, LESS current (6/30) drops the entire voltage. It means that charge is more susceptible to losing the energy it carries when moving through a higher resistance.

Make any sense?

Thanks for all your answers people. That's a really good way of putting it and I have not seen it put like that before. I think it makes sense, so your basically saying that with a lower resistance it takes a higher current to dissipate that energy? Is it right to think of the reason for transferring energy to be due to collisions of the electrons with the atoms of the resistor? I'm just trying think that if they are colliding with the atoms then they must lose energy and slow down but still maintain the same current. I was thinking they might have a higher drift velocity through the resistor but how can they be transferring energy and slowing down AND be drifting faster?

## 1. What is resistance?

Resistance is a measure of how much a material or object opposes the flow of electrical current. It is measured in ohms (Ω) and is dependent on factors such as the material's conductivity and dimensions.

## 2. How is resistance calculated?

Resistance can be calculated using Ohm's law, which states that resistance is equal to voltage divided by current (R = V/I). It can also be calculated using the equation R = ρL/A, where ρ is the material's resistivity, L is the length of the material, and A is the cross-sectional area.

## 3. What factors affect resistance?

The main factors that affect resistance are the material's resistivity, length, and cross-sectional area. Temperature can also have an impact on resistance, as well as the presence of impurities or defects in the material.

## 4. How does resistance affect electrical circuits?

Resistance plays a crucial role in electrical circuits as it determines the amount of current that can flow through a circuit. Higher resistance means less current can flow, while lower resistance allows for more current to flow. This can affect the overall functioning and efficiency of the circuit.

## 5. How can resistance be reduced in a circuit?

There are a few ways to reduce resistance in a circuit. One way is to use materials with lower resistivity, such as copper or silver. Another way is to increase the cross-sectional area of the material. Additionally, keeping the temperature low and minimizing impurities can also help reduce resistance in a circuit.

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