E3. Current, Resistance

and Ohm's Law. This is a very common law in physics, and to understand it, we have to cover two more units: Current and Resistance, which come up often in other parts of electricity in Physics.

What is Current?

Current is a measure of the rate at which current flows, meaning how fast current flows, and is measured in the unit of Amps (A).

• Let’s say we had a circuit, with electrons flowing through the wires. Our Charge is based on the number of electrons, and the speed at which they move around the circuit is our Current.

• We can calculate Current as ΔQ/Δt

  • Using our previous definition, we measure the rate at which a charge Q, so how fast the charge Q moves around the circuit.

---

What is Resistance?

• Resistance, in simplest terms, is a measure of how difficult it is for some current, to flow through a material, and is dependent on certain material properties. We measure the resistance of a material in the unit of Ohms (Ω).

• To understand which properties affect the resistance a material experiences, we have two sets of equations that we use:

  

  1. R = pL/A ]→ Resistance = Density * Length / Cross-Sectional Area

     1. This equation shows that as the density of a material increases, or the length of the wire increases, the resistance will increase, whilst increasing our Cross-Sectional Area will decrease our resistance.

     2. We can understand this by imagining a tunnel we crawl through. Having a tunnel with a larger Cross-Sectional Area would make fitting through and crawling easier. As for the length, imagine having to crawl further: You would crawl more closely to conserve energy.

        The density here has a more complex reason, which only makes sense in terms of a circuit: Metals have free-floating electrons that can move throughout the metal, and having a denser metal means that more of the electrons can move freely in the same area, so being denser means there are more electrons than able to move throughout the circuit, which would increase the Current.

2. Rt = Ro(1 + 𝛼ΔT) ]→ Final Resistance = Initial Resistance * (1 + (Temperature Coefficient * Change in Temperature))

   • This law explores how an increase in temperature will affect a material’s resistance. Ro here just measures our Initial Resistance, so the resistance of a material before a temperature change. ΔT here represents our Temperature Change, where if a material heats up, it’s positive, but if a material is cooling down, it’s negative, and 𝛼 is something known as our ‘Temperature Constant’.

   • Temperature Constant is specific to each unit and measures how a change in temperature will affect its resistance.

---

Ohm’s Law

This is a physics equation that was made by a physicist named Simon Ohm, and it related Potential Difference (V) to Current (I) and Resistance (R). Ohm’s Law is:

• V = IR ]→ Potential Difference = Current * Resistance

  • We’ve brought a quantity we last introduced: Potential Difference (The Work Done to move some amount of charge from one area to another).

  • This equation states that Potential Difference is the product of Current and Resistance, which means that if one of them were to increase, and the other didn’t change, the Potential Difference would increase.

  • The main real-life application would be in a situation where we have a constant Potential Difference, say a computer connected to the mains with a plug, where the computer receives a constant Voltage, up to 110 or 220V, depending on where you live.

    • For a Constant Potential Difference, changing either the Current or Resistance will end up having the exact opposite on the other value. Let’s say we double our Current, but we have the same Potential Difference: The resistance must’ve been lower for it to conform to existing laws of physics.

    • Similarly, if we were to triple the resistance, but didn’t supply any extra Potential Difference, we would need to have a third of our existing Current for it to fit with existing laws of physics, namely the Conservation of Charge (Total charge of a system, like a circuit, won’t change, it can just get transferred/moved from one area to another)

---

To recap, we’ve covered:

1. What is Current + The Equation (ΔQ/Δt)

2. What is Resistance + 2 Equations to Calculate it | (Rt = Ro(1 + 𝛼ΔT)) if we use temperature, and (R = pL/A) otherwise.

3. Ohms’ Law (V = IR)