## Homework Helpers: Physics

**6 Electric Current and Circuits**

**Lesson 6–2: Resistance**

When we discussed the construction of our imaginary flashlight in our last lesson, we said that the bulb converts some of the electric potential energy of the charges into heat and light. The reason this happens is because the filament used inside the bulb offer more resistance to the motion of the charges than the copper wire that is used to connect the battery to the bulb. In physics, **resistance** is defined as the opposition to the flow of charges through a conductor. If you rub your hands vigorously together, you notice that they get hotter. In fact, you may have done this many times when you were outside in the cold without gloves. The friction between your hands converts some of the kinetic energy of the motion into heat. The filament of the bulb does essentially the same thing, converting electrical energy into heat and light.

In our water analogy, resistance might be thought of as a partial blockage in a pipe that decreases the rate of the flow of the water. In terms of electricity, the resistance of a material is defined as the ratio of the potential difference across the material to the current through the material.

or

**This relationship is known as Ohm’s law**, and it is one of the most important formulas you need to use when you study electricity in physics. The resistance of a material is measured in ohms (Ω), which are equivalent to volts/amps.

**Example 1**

Find the current through a bulb that has a resistance of 3.0Ω and a potential difference of 9.0 V across it.

Ohm’s law is not really a universal or fundamental law, as not all materials “obey” it. Materials that follow Ohm’s law over a wide range of potential differences are called **ohmic materials**. Materials such as semiconductors, which don’t follow Ohm’s law over a wide range of potential differences, are called **nonohmic**.

In reality, the copper wire in our flashlight actually offers a small amount of resistance to the charges. The resistance is relatively low, so the wire is considered a **conductor**. A conductor is a material that allows charges to move freely through it. In addition to conductors and resistors, there are **semiconductors**, which conduct electricity better than resistors, but not as well as conductors.

Four factors affect the resistance of a component:

1. The **material** the component is made of. For example, copper is a good conductor, offering less resistance than a material such as tungsten.

2. The **temperature** of the component. The molecules of a hot material exhibit more motion, leading to more collisions with charges, resulting in greater resistance.

3. The **cross-sectional area** of the component. Just as a wider pipe allows for a greater flow of water, a wider wire offers less resistance, allowing for a greater flow of charge.

4. The **length** of the component. For example, using a very long extension cord for an electric hedge-trimmer results in greater resistance, decreased current, and decreased power.

**Resistivity**

At a given temperature, the resistance offered by a material will be proportional to its length and inversely proportional to its cross-sectional area.

If we insert the proportionality constant for a given material into the formula, we can set the sides equal to each other.

This quantity (*ρ*) is not a true constant, because it varies from material to material and from temperature to temperature. We call this quantity resistivity (*ρ*), and it is measured inΩ· *m*.

**Example 2**

A wire with a length of 0.895 m and a cross-sectional area of 1.0 × 10^{–7} m^{2} has a current of 1.00 × 10^{2} A through it and a potential difference of 9.0 V across it. Find the resistivity of the wire.

**Find:** *ρ*

As you can see, we don’t have quite enough “givens” to solve for resistivity using only our resistivity formula, as we are missing both *ρ* and R. We can use Ohm’s law to find R, because we have also been given I and ΔV.

**Resistors**

We said that bulbs could be considered resistors because they resist the flow of charge through them. They are not, however, the only type of resistors. There are also components whose sole purpose is to add resistance to a circuit. Adding resistance to the circuit will decrease the current and protect other components from overloading.

Lesson 6–2 Review

__1.__ _______________ is the opposition to the flow of electric current.

__2.__ A component has a potential difference of 3.0 V across it and a current of 2.0 A through it. Calculate its resistance.

__3.__ Find the current through a 3.0 *Ω* resistor with a voltage of 1.5 V across it.