In this explainer, we will learn what electrical resistance is and how it affects the flow of charge within a circuit.

Electrical resistance, which we often just call “resistance,” is opposition to the flow of charge. The electrical resistance of a component or object describes how difficult it is for electrons to flow through it.

To illustrate what electrical resistance is, let’s imagine we have two identical rods of metal, but one is made of copper and the other is made of iron. The rods are each connected to an identical cell, as shown in the diagram below, with each cell creating a potential difference of 1 V across each rod.

In this scenario, we actually find that the iron rod has a much smaller current in it, even though each rod has the same
potential difference between its ends. It seems that it is more difficult for electrons to travel along the iron rod
than the copper rod. We can describe this behavior by saying that the iron rod has a **higher electrical resistance**
than the copper rod.

When charge flows through an object with resistance, electrical energy is dissipated as thermal energy. This is why very large currents can cause wires and components to become hot.

Electrical resistance is measured in units called ohms. We represent with the symbol Ω, which is the Greek capital letter “omega.” When we are writing equations in physics, we represent resistance with the symbol . So, for example, if an object had a resistance of 5 ohms, we could write meaning “the resistance is equal to 5 ohms.”

The resistance of a piece of solid material (such as a block of metal or a wire) depends partly on its shape and partly on the properties of the material it is made from.

Let’s consider the copper rod from our earlier example. If we compared this to a copper rod with a greater diameter, as in the following figure, we would find that the rod with the greater diameter has a smaller resistance. So, in these circuits, we find that the rod with a greater diameter has a greater current in it than the narrower rod.

If we compared the original copper rod with a copper rod that has the same diameter but a greater length, as in the next figure, we would find that the longer rod has a greater resistance. So, in these circuits, we would find that the longer rod has a smaller current in it than the shorter rod.

### Example 1: Comparing the Electrical Resistances of Wires with Different Lengths

Any wire will have some amount of resistance. There are two unequal lengths of identical wire. Which one of the following sentences is correct?

- The wire of greater length has the greater resistance.
- The wire of greater length has the lower resistance.
- Both wires will have the same resistance.

### Answer

In this question, we are asked to compare the resistances of two wires that have different lengths but that are otherwise identical. To answer this question, we need to know that the resistance of a piece of material is determined partly by its shape. Since a wire is essentially a long, thin piece of metal, this means that the resistance of a wire is affected by its shape.

Electrical resistance is a measure of opposition to current. So let’s consider what would happen if we had a current in each wire.

The question points out that *any* wire will have some amount of resistance, so the electrons in each wire would
experience opposition to their motion as they travel along the wires. Because an electron flowing through a *long*
wire will have to pass through *more wire* than an electron flowing through a short wire, this means that longer
wires have *more resistance* than short wires. So, the correct answer to our question is option A: the wire of
greater length has the greater resistance.

Electrical resistance plays an important role in circuits. When we design circuits, we use resistance to control the flow
of charge. We do this by using components called **resistors**. Resistors are simply components that have electrical
resistance—they do not perform any other function.

When we are drawing circuit diagrams, we represent resistors using a zigzag like this:

The circuit diagram below shows a resistor connected in a circuit with a cell.

All objects, including electrical components, have a resistance. This means that many components effectively act the same as resistors in a circuit. A light bulb with a resistance of 5 Ω, for example, acts exactly like a resistor with a resistance of 5 Ω. The difference is just that the bulb also emits light!

We can measure the resistance of a component using a device called an ohmmeter. The diagram below shows how an ohmmeter is connected to a resistor to measure its resistance.

There is a special type of resistor known as a **variable resistor**. The resistance of a variable resistor can be changed,
often by turning a knob or using a slider. The circuit symbol for a variable resistor is the same as the symbol for a resistor
but with a diagonal arrow through it as shown below.

### Example 2: Identifying Variable Resistors in a Circuit Diagram

The diagram below shows an electric circuit. How many variable resistors are there in the circuit?

### Answer

In this question, we have been given a circuit diagram, and we need to identify how many variable resistors it contains. As we can see, this diagram is quite complicated and contains many different components, some of which we might not have seen before!

However, to answer this question, we just need to know that the symbol for a variable resistor looks like this:

Looking at the circuit diagram in the question, we can see that this symbol occurs in three places.

So, in conclusion, the circuit diagram contains **three** variable resistors.

Although all objects have resistance, some electrical components have such small resistances that we can consider their
resistance to be zero when we are dealing with circuits. Two common examples include **wires** and **cells**. Even
though we know that these components *do* have resistance in real life, we almost always assume these components
have zero resistance when we are analyzing circuits. This makes things much easier to work out!

In practice, the size of the current in a component is determined by two things: the potential difference across the component and the resistance of the component.

Increasing the voltage and increasing the resistance have opposite effects on the current. Increasing the potential difference across the component will increase the current. But increasing the resistance of the component will oppose the flow of charge and therefore decrease the current.

Current, potential difference, and resistance are three very important concepts in electricity. The units that we use for each of these quantities (amperes, volts, and ohms) are balanced so that a potential difference of 1 V across a component with a resistance of 1 Ω will produce a current of exactly 1 A.

### Example 3: Finding the Resistance of a Component from the Current and Potential Difference

The diagram below shows an electric circuit consisting of a cell and a bulb. If the potential difference across the bulb is 1 volt and the current through the bulb is 1 ampere, what is the resistance of the bulb?

### Answer

In the circuit diagram, we can see a bulb connected to a cell. In the circuit, the cell applies a potential difference across the bulb, which causes charge to flow through it. This in turn causes the bulb to light up.

The rate at which charge flows through the bulb—that is, the current—is determined by two things: the potential difference across the bulb and the resistance of the bulb. The potential difference across the bulb describes how hard electrons are being “pushed” through the bulb, while the resistance of the bulb describes how much the bulb opposes this motion of the electrons.

The units we use to measure current, potential difference, and resistance are “balanced” so that a potential difference of 1 V across a component with a resistance of 1 Ω will produce a current of exactly 1 A. Since we are told the bulb in the question has a potential difference of 1 volt across it and a current of 1 ampere through it, this means that its resistance must be exactly 1 ohm.

### Key Points

- Electrical resistance (or just “resistance”) is opposition to the flow of charge. Electrical resistance is measured in ohms, represented by the symbol Ω. In equations, we represent resistance with the symbol .
- Resistors are components with electrical resistance. The following symbol is used to represent a resistor in a circuit diagram.
- Variable resistors are a special type of resistor whose resistance can be changed. The following symbol is used to represent a variable resistor in a circuit diagram.
- All objects have a resistance. However, to make circuit analysis simpler, we generally assume that wires and cells in circuit diagrams do not have a resistance. Applying a potential difference of 1 V across a component with a resistance of 1 Ω will produce a current of exactly 1 A within the component.