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Voltage (Chapter 2: Theory)

In this article we will discuss:

- The Mechanisms of Voltage

- An Equation and the Definition of Voltage

- The Generalised Power Law

- Combining Batteries

Mechanisms of Voltage

The first thing to understand is that for current to flow, the battery needs the circuit as much as the circuit needs the battery. They are dependent on each other.

In a nutshell, chemical reactions in the battery leads to a build-up of electrons on the negative terminal. These electrons then are transferred, by the circuit, to the positive terminal where further chemical reactions occur. Hence, without this transfer of electrons, the chemical reactions could not take place and current would not flow. The positive and negative terminals must be linked.

These free electrons at the negative terminal repel each other. This could be thought of as a type of pressure, an electrical pressure which is alleviated by the electrons as they disperse around the circuit. This is analogous to water in a hosepipe. The water is at high pressure when it leaves the nozzle, but the pressure the water is under decreases as it is disperses in the air.

This "electrical pressure" can be formally expressed as a quantity called "potential energy". Where there is a high amount of electrical pressure, the electrons have a high potential energy.

Some of this repulsive energy is absorbed by material and collisions in the circuit. This results in areas of the circuit with low electrical pressure. They, therefore, have low potential energy and so are less able to do work and give (after experiencing) a weaker shoving action (repulsive action).

This can be seen in a circuit with a light bulb and a battery. All loss of electrical energy is assumed to have occurred in the light bulb, where electric potential energy is converted into heat and light. The wires are assumed to have no resistance so no energy is transferred and so no electrical pressure is lost.

Note: As similar charges move closer together, the electrical potential energy increases. As the similar charges move further away, the potential energy decreases.

An Equation and the Definition of Voltage

The voltage is also known as the potential difference because it is the difference between the electrical potential energies of two unit charges at two different points in the circuit.

When a voltage is applied across a conductor, this gives rise to an electromotive force which gives all free electrons in the conductor a push. If we think of our battery again, there is a high potential energy at the negative terminal (as there are all those like charges next to each other) and none at the positive terminal. Thus, there is a potential difference (voltage) so an electromotive force (like charges repelling each other around the circuit).

If we take point A as being at the negative terminal and point B as being at the positive terminal. The voltage across A and B is the difference is potential energy between point A and point B per unit charge. So:

Voltage = difference in energy/charge

Voltage is measured in volts. Two points with a voltage of 1 V between them have enough "pressure" to perform 1 J of work moving 1 C of charge.

The Generalised Power Law

If we assume that an electron loses all of its potential energy. Since power = energy transferred (or work done)/time taken (P = E/t). U is potential energy.

P = dW/dt = dU/dt = V(dq/dt) = IV.

P = IV is known as the Generalised Power Law.

A circuit undergoes 1 W of power loss when there is 1 A flowing through the circuit and 1 V across it.

Combining Batteries

If we put two batteries in series with each other, the voltage of the circuit is doubled. This can be seen because twice the number of electrons are produced by the batteries, so we double the number of electrons pumped into the circuit.

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