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# Resistance and Ohm's Law for AP Physics B & C

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By McGraw-Hill Professional
Updated on Feb 12, 2011

Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C

### Current

A circuit is simply any path that will allow charge to flow.

Technically, a current is defined as the flow of positive charge. We don't think this makes sense, because electrons—and not protons or positrons—are what flow in a circuit. But physicists have their rationale, and no matter how wacky, we won't argue with it.

In more mathematical terms, current is defined as follows:

What this means is that the current, I, equals the amount of charge flowing past a certain point divided by the time interval during which you're making your measurement. This definition tells us that current is measured in coulombs/second. 1 C/s = 1 ampere, abbreviated as 1 A.

You've probably noticed that just about every circuit drawn in your physics book contains a battery. The reason most circuits contain a battery is because batteries create a potential difference between one end of the circuit and the other. In other words, if you connect the terminals of a battery with a wire, the part of the wire attached to the "+" terminal will have a higher electric potential than the part of the wire attached to the "–" terminal. And positive charge flows from high potential to low potential. So, in order to create a current, you need a battery (see Figure 21.1).

In general, the greater the potential difference between the terminals of the battery, the more current flows.

The amount of current that flows in a circuit is also determined by the resistance of the circuit.

Resistance is measured in ohms. 1 ohm is abbreviated as 1 Ω.

If we have some length of wire, then the resistance of that wire can be calculated. Three physical properties of the wire affect its resistance:

• The material the wire is made out of: the resistivity, ρ, of a material is an intrinsic property of that material. Good conducting materials, like gold, have low resistivities.1
• The length of the wire, L: the longer the wire, the more resistance it has.
• The cross-sectional area A of the wire: the wider the wire, the less resistance it has.

We put all of these properties together in the equation for resistance of a wire:

Now, this equation is useful only when you need to calculate the resistance of a wire from scratch. Usually, on the AP exam or in the laboratory, you will be using resistors that have a pre-measured resistance.

Resistors are typically ceramic, a material that doesn't allow current to flow through it very easily. Another common type of resistor is the filament in a light bulb. When current flows into a light bulb, it gets held up in the filament. While it's hanging out in the filament, it makes the filament extremely hot, and the filament gives off light.

To understand resistance, an analogy is helpful. A circuit is like a network of pipes. The current is like the water that flows through the pipes, and the battery is like the pump that keeps the water flowing. If you wanted to impede the flow, you would add some narrow sections to your network of pipes. These narrow sections are your resistors (see Figure 21.2).

The way that a resistor (or a bunch of resistors) affects the current in a circuit is described by Ohm's law.

V is the voltage across the part of the circuit you're looking at, I is the current flowing through that part of the circuit, and R is the resistance in that part of the circuit. Ohm's law is the most important equation when it comes to circuits, so make sure you know it well.

When current flows through a resistor, electrical energy is being converted into heat energy. The rate at which this conversion occurs is called the power dissipated by a resistor. This power can be found with the equation

This equation says that the power, P, dissipated in part of a circuit equals the current flowing through that part of the circuit multiplied by the voltage across that part of the circuit.

Using Ohm's law, it can be easily shown that IV = I2R = V2/R. It's only worth memorizing the first form of the equation, but any one of these could be useful.

Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C

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