Summary for Chapter 23: Electric Current

Current

An electric current is a flow of electric charge. The flow or movement of charge is usually driven by a difference in potential. Consider two points A and B. If the potential at A is greater than the potential at B, positive charge will want to move from A to B and negative charge will want to move from B to A. If positive charge moves from A to B we say there is a current flowing from A to B.

• The current is the amount of charge that moves from A to B per second, or

• If 6Coulombs of charge moves from A to B in 3seconds, the current is 6C/3s = 2(C/s). A Coulomb per Second is an Ampere or A. So the current is 2A.
• Currents are driven by differences in potential, often called a voltage or a voltage difference. If the potential is the same at two points, e.g. A and B, the electric force does not "push" the charge between those two points. If the potentials are different, the electric force pushes the charge between them.
• The amount of current depends on how large the potential difference is and on the material the charge must travel through to get from A to B.

Circuits

• There are several ways of producing potential differences. Batteries do it chemically, chemical reactions produce the potential difference. Most of our electric power comes from "magnetic" effects, rotating magnets in a coil of wires will produce a potential difference. The symbol for a battery is shown at the right.
• The + indicates the positive terminal and the - the negative terminal. The potential difference is measured in Volts, and is sometimes called the Voltage. A typical battery (AA, C, and D cells) produce a potential difference, or voltage, of about 1.5Volts.
• A typical circuit would look like the one at the right. (This is typical of a flashlight). A conducting wire (usually made of copper) connects the terminals of the battery to the light bulb's two terminals. In-between the terminals of the bulb is another metal wire, usually not as good a conductor as copper. Thus there is a complete path for the electrons to flow from B through the light bulb to A. When they get to A, the battery "pumps" them back to B (remember electrons at B have a higher potential energy than those at A.) To do this the battery does work on them. (It is just like pumping water uphill, a pump has to do work on the water to increase its potential energy.)
• If the conducting path is broken, charge will not flow. If the conducting path is complete or not broken it is said to be closed (i.e. a closed path). If it is broken it is said to be open.

Resistance

• The amount of current depends on how large the potential difference is and on the material the charge must travel through to get from A to B. Some materials resist the flow of charge more than others. We characterize this resistance by measuring the current that flows between A and B through the material for a given difference in potential. The resistance is

• This has units of Volts per Amp (V/A) which is usually called Ohms. For many materials the resistance only depends on the size and shape of the object, so for a fixed type of material and a fixed size and shape, the current is directly proportional to the difference in potential, or the Voltage. If the voltage is doubled, the current doubles. If the voltage triples the current triples.
• If an object has a large resistance, it means it is hard to push current through it.
If the voltage across a resistor is 3V and the current is 0.1A, the resistance is 3V/(0.1A) = 30(V/A) or 30 Ohms.

### Series and Parallel Circuits

When current flows in circuits, there is often more than one element in the circuit that the current can go through.  There are two common configurations, parallel and series.

In series circuits, all the current must flow through each element.  Then the voltage across each element will be different than the total voltage, but the total voltage will be the sum of the individual voltages.  (One can say they have equal currents but different voltages.)  In the picture at the right, all the current that goes out the + terminal must pass through BOTH A and B to get to the - terminal.

In parallel circuits, the voltage across each element is the same, but the currents are different.  The total current in the circuit is the sum of the currents through each element.  In the picture at the right, the current coming from the + terminal can divide at point 1 and go through either Bulb A OR Bulb B to get to the - terminal.  Here the voltage across each bulb is the same, the voltage of the battery, VB.  In household wiring the circuits are usually parallel circuits, so each element will have the same voltage across it.

Work and Power

• When current flows through a resistor, the potential energy of the charge drops. If a charge Q drops in potential by V, its potential energy drops by Q times V, or QV. Where does this energy go?  In a resister is becomes heat to increase the temperature of the resistor. (In other types of circuits we can get use this energy to do work for us, e.g. electric motors.) This energy comes from the battery. The rate at which the battery is supplying energy to the circuit is I times V, or IV, where I is the current and V is the "voltage" of the battery.
• A 1.5V battery supplying 0.25A of current to a light bulb is supplying 1.5x0.25VA of Power, or 0.375W or 0.375J/s. This heat makes the light bulb's filament so hot that the thermal, or blackbody, radiation it produces is visible.