2-5 Resistance

What is Resistance?

Consider a fire hydrant and a garden hose. Which allows more water through? Both are connected to the same municipal water supply.

If you said the fire hydrant, you're right. It is a lot easier for water to flow through the fire hydrant; we say that it has a lower resistance to the flow of water.

Now think about a night light and a spotlight. Which puts out more light? Both are plugged into the same wall outlet.

If you said the spotlight, you're right again. Much more light comes out of it, enough to light up an entire stage. We say that the spotlight has a lower electrical resistance than the night light does: it's easier for current to flow through the spotlight.

(Here, when we talk about "resistance," we're going to be talking only about "electrical resistance." Nothing more about water, really.)

But if we look at a circuit diagram for both the night light and the spotlight, it will basically look the same:

The source on the left is an "AC source" instead of a battery. Here, AC stands for alternating current, and it's something strange that the electricity in the walls does. It alternates, or flips, the direction of the current many times per second: 60 times per second in North America.

As it turns out, current that alternates direction travels through long wires much more efficiently than DC, or direct current, the kind that comes from cells and batteries. If you live more than a couple of kilometres from a power plant, and most of us do, it makes much more sense to have the electricity between the plant and your home to be AC through the wires.

Some of your plug-in electrical devices convert AC to DC inside, but others run just fine on AC. For our purposes, it doesn't really matter -- and besides, this section is about resistance anyway.

The point is that the voltage across the two wires that plug into the wall is the same for both: about 120 volts.

Notice the "AC" on the screen, and how the dial is measuring volts ("V") with a squiggle ("~") on top? That's AC.

Resistors

So there must be something very different about both lights. And there is, because the night light has a resistor in the circuit as well. Here are a few resistors you might find in electronic devices:

These devices are not exciting. They don't light up, they don't play a sound or shake. All they do is go into the circuit, resist the flow of current, and get a little warm to the touch. The different colours are part of an international code which states how much the resistors resist current.

Here's the actual circuit diagram:

The resistor is shown in the circuit diagram with a symbol that looks like a jagged set of bumps. It might be useful to think of them like "speed bumps" that you see on streets, increasing the resistance of cars to move down that street quickly.

Here's a video that shows how resistors can affect the flow of something. In the video, marbles take the place of electrons, and the shape of the sides of the "wire," along with things put in the middle of the path, affect the resistance of the marbles to flow.

Don't worry too much about "resistivity" or any equations -- the flowing of marbles here is just a really nice way to think about electricity and resistors!

Ohm's Law

In the mid-1820s, German physicist Georg Ohm found a relationship between the voltage drop across (V) and the current through (I) a load.

Let's say you have two resistors, R₁ and R₂, hooked up to identical sources.

Both the sources have voltage gains of V₀, so it's the same "pushing force" behind the current. Consider this:

• R₁ has a high resistance, which means it's tough for the current to get through it.

• R₂ has a low resistance, which means it's easy for the current to get through it.

Ohm found that, for most materials, if the resistance was doubled, half the current would get through. If resistance was increased by 10 times, current would be one-tenth what it was before. In short:

The bigger the resistance,

the smaller the current

(if the voltage is the same).

If a resistor followed this rule exactly, it is said to obey Ohm's Law. We can also say that resistor is ohmic -- in this course, unless a resistor is specifically said to be non-ohmic, assume it obeys that rule.

The Resistance Equation

A lot of sources of physics information say that the following equation is "Ohm's Law," but that's not quite correct. The equation below is the definition of resistance.

Voltage (V, measured in volts, V) and current (I, measured in amps, A) go into the equation, and resistance (R comes out.

The unit we use to measure resistance is the ohm, named after Georg Ohm. The symbol we use for it is a Greek letter, the capital letter "omega," which looks like a horseshoe with feet: Ω. So, if we want to say the resistance of a load is 15 ohms, we write it like this: R = 15 Ω

Example: A light bulb has a current of 0.75 A through it, and has a voltage drop of 4.5 V. What is the light bulb's resistance, in ohms?

I = 0.75 A

V = 4.5 V

R = ?

R = V/I = (4.5 V)/(0.75 A) = 6.0 Ω

Here's a video showing how to use the resistance formula, in all three ways, using a "formula triangle." It is expected that you should be able to rearrange the R = V/I formula properly, but if that's a struggle, a formula triangle like this will work.

Practice

The Basics

1. Draw a circuit diagram, using proper symbols, showing a 3-cell battery, a switch, and three resistors in series. Label the resistors R₁, R₂ and R₃.

2. Calculate the resistance of an electric fan, which runs on a 3.8 V battery, if the current through the fan is 0.28 A.

3. Fill in the blank: "If the resistance of a load is low, the current through it will be ______________ ."

Extensions

1. The resistance of a blender is 14 Ω. The voltage drop across it is 220 V, because it's in Europe (in North America it would be 120 V). What is the current through the blender?

2. If three resistors, each with R = 10 Ω, are in series, would the total resistance of the resistors together be greater than 10 Ω, 10 Ω exactly, or less than 10 Ω?

3. What about if those resistors were in parallel?