13.3 Resistance

Resistance

The resistance of a circuit element can be thought of as how much it opposes the flow of electric current in the circuit.

Resistance

The resistance of a conductor is defined as the potential difference across it divided by the current flowing though it. We use the symbol R to show resistance and it is measured in units called Ohms with the symbol $\mathrm{\Omega }$ .

$$1\mathrm{Ohm}=1\frac{\mathrm{Volt}}{\mathrm{Ampere}}.$$

What causes resistance?

We have spoken about resistors that reduce the flow of charge in a conductor. On a microscopic level, electrons moving throughthe conductor collide with the particles of which the conductor (metal) is made. When they collide, they transfer kinetic energy.The electrons lose kinetic energy and slow down. This leads to resistance. The transferred energy causes the resistor to heat up.You can feel this directly if you touch a cellphone charger when you are charging a cell phone - the charger gets warm because its circuits have some resistors in them!

All conductors have some resistance. For example, a piece of wire has less resistance than a light bulb, but both have resistance. A lightbulb is a very thin wire surrounded by a glass housing The high resistance of the filament (small wire) in a lightbulb causes the electrons totransfer a lot of their kinetic energy in the form of heat Flourescent lightbulbs do not use thin wires; they use the fact that certain gases glow when a current flows through them. They are much more efficient (much less resistance) than lightbulbs. . The heat energy is enough to cause the filament to glow white-hot which produces light. The wiresconnecting the lamp to the cell or battery hardly even get warm while conducting the same amount of current. This is because of theirmuch lower resistance due to their larger cross-section (they are thicker).

An important effect of a resistor is that it converts electrical energy into heat energy. Light is a by-product of the heat that is produced.

Why do batteries go flat?

A battery stores chemical potential energy. When it is connected in a circuit, a chemical reaction takes place inside the battery which converts chemical potential energy to electrical energy which powers the charges (electrons) to move through the circuit. All the circuit elements (such as the conducting leads, resistors and lightbulbs) have some resistance to the flow of charge and convert the electrical energy to heat and, in the case of the lightbulb, heat and light. Since energy is always conserved, the battery goes flat when all its chemical potential energy has been converted into other forms of energy.

Resistors in electric circuits

It is important to understand what effect adding resistors to a circuit has on the total resistance of a circuit and on the current that can flow in the circuit.

Resistors in series

When we add resistors in series to a circuit, we increase the resistance to the flow of current. There is only one path along which the current can flow and the current is the same at all places in the series circuit. Take a look at the diagram below: On the left there is a circuit with a single resistor and a battery. No matter where we measure the current, it is the same in a series circuit. On the right, we have added a second resistor in series to the circuit. The total resistance of the circuit has increased and you can see from the reading on the ammeter that the current in the circuit has decreased and is still the same everywhere in the circuit.