Basic Electrical Circuits

An electrical circuit is any combination of wires and electrical devices (also called circuit elements) through which current can flow. We will begin with a typical flashlight powered by two 1.5 V AA batteries.

Below is diagram of the actual flashlight next to a schematic diagram. Note the symbols used to denote the batteries and the switch. The general symbol for any resistor is just , the oval shown below indicates that it is also a light bulb. (Check out the standard electrical symbols listing.) The switch is shown in the "open" position. That is, the flashlight is off and the circuit is broken or not complete. No current can flow until there is a path. Charge will not flow from one side of the battery unless and equal amount can flow into the other side! When the switch is in the "closed" position, the flashlight is on and there is a path for the current to flow. (Although there is no set rule, switches are usually shown in the open position in schematics.)

The batteries are called DC sources. DC or "Direct Current" means that current flows just one way. Which way? Positive current, also called conventional current, flows out of the positive side of the battery (indicated by the longer line) and into the negative (indicated by the shorter line). And what do we mean by positive current? It is positive charge flowing as the arrows show.

Foul you cry! Yes, we now know that what actually happens is that electrons (negative charge) flow out of the negative side and into the positive. But in the late 1700's Ben Franklin, a scientist as well as a statesman, had no way of knowing that. He made a guess at what was happening and we're stuck with it. But it doesn't change any of the physics. So, from hence forth, we pretend positive charge flows out of the positive side of the battery.

Series Circuit

The two batteries are connected in series, that is, one after another. The current that flows through one must also flow through the other. What does that mean for the voltage? Think of climbing a 1.5 ft step and then following it with another 1.5 ft step. Your are now 1.5 + 1.5 = 3.0 ft higher. Similarly, the potential from the negative side of the first battery to the positive side of the second is 1.5 V + 1.5 V = 3.0 V. The potential across any two or more elements connected in series is always the sum of the individual voltages.

What potential is across the lightbulb of the flashlight shown above? The resistance in the "wires" that provide the connections between the batteries and bulb should be much lower than that of the bulb itself. Therefore, there is negligible "potential drop" across the wires. Essentially all 3.0 V provided by the batteries will be across the bulb. Later, we will address the role that resistance in the wires play. But for now, let's assume all potential drops are across the circuit elements. Note that the bulb is in series with the batteries. The current that flows throught the batteries is the same that flows through the bulb. The current has no other path.

There is a method for understanding potential drops. The total potential drop around a complete circuit must be zero. (This similar to saying that the sum of all height changes on a round-trip hike must sum to zero.) As we move across the batteries, we gain potential of 1.5 V each (for a total of 3.0 V), followed by the potential across the bulb ... then we are back to where we started. (Don't forget that potential change along the wires is essentially zero.) Therefore, the potential across the bulb must be a 3.0 V drop.

Let's apply the formulas from the previous section.

Problem: If the bulb in the flashlight above has resistance 2 W, then what current flows through the bulb and what power does it consume?

Solution: The current flowing through the bulb is I = 3.0 V / 2 W = 1.5 A. The power being consumed by the bulb is P = I² R = (1.5 A)² x 2 W = 4.5 W. The power being supplied by the two batteries is P = I V = (1.5 A) x (3.0 V) = 4.5 W. It should be no surprise that the power consumed by the bulb is equal to that supplied by the batteries.

Parallel Circuit

Elements in a circuit are in parallel when they are connected in such a way that the potential across them is always the same. Essentially, the ends of each element are connected together. Let's consider two important cases.

The Car - Consider the simplified diagram for the electrical system of a car. Notice that all the elements receive a full 12 V from the car battery.

The current that flows out of the battery can split up and flow to each element individually. Each element will receive a different portion of the total current, according to its resistance, but each element receives the same 12 V. The elements are in parallel with one another when the switches are closed. Note that each switch is in series with the element it controls. Do you understand why a switch must be in series with the device it controls? (Actually, this is not absolutely true. In lab, you will have the chance to observe such an exception.)

Look at the diagram and see if you can understand the effect of each switch. Can you identify which one represents the key ignition switch? Is this consistent with your experience of what can be turned on with your car key? (A more proper diagram would show the ignition and starter switches as part of one compound switch.)

Summarizing Series and parallel circuits ... Elements in series have the same current, but the voltage drops may be different. Elements in parallel have the same voltage, but the currents may be different. Here's an important difference to remember. Elements in parallel can be operated independently, while elements in series cannot.

The Home - Are the electrical elements in your house (the fridge, the toaster, the lights, etc) in series or parallel? They better be in parallel, right? The electrical diagram below shows the wiring for a typical room in a home. In this example, a single power line, consisting of a red wire and a green wire, services the six outlets and two overhead light fixtures. You may think of the red wire as if it were connected to the positive terminal of 120 V battery while the green wire is connected to the negative side . This is not correct, but we will deal with the details of the AC power in your home in the next section.

All the outlets and the light fixtures (with their switches) are connected in parallel. However, the switches are in series with the lights they control. If the switch is closed, the red wire coming into the switch from the power line is connected to the red wire going out to the light, and the light will be on. If the switch is opened, there is no connection and the light is off. The green wire from the other side of the light fixture is connected directly to the green wire of the power line.

In the simplified diagram above, it may not appear that the outlets are in parallel, but they are. Most outlets provide two screwposts on each side of the casing, like that shown in the picture to the right. Both screwposts on a side are connect to the "slot" on that side. That makes it convenient to run a line into the outlet, say at the bottom posts, and then run a line out to the next outlet from the top posts. When an appliance is plugged into the outlet, it will be in parallel with all the other outlets, lights, etc. (Of course, the appliance may contain its own switch.) The colors for the wires in the diagram above were chosen for clarity. The colors you are most likely to find in household wiring is discussed in AWG and household wiring. A few notes: The longer slot is connected to the O V wire. This is the convention for the somewhat new "polarized" plug. The extra copper ground wire shown the the right is discussed in the "AWG and household wiring" link above. The outlet in the upper left corner of the room electrical diagram is at the "end of the line". One of the screwposts on either side will not be used. Two or more lines may service a room if the electrical needs are particularly high. The kitchen usually has separate lines to the refrigerator, the stove, and the outlets.

Problem: Let's put a few numbers to the car circuit example. Assume we have a 10 W dome light, a 50 W radio, and two headlights at 300 W each. What current do they draw?

Solution: For the dome light, P = I V, so I = P/V = 10 W / 12V = .83 A. The radio consumes 50 W, so I = 50 W / 12 V = 4.2 A. The headlights are rated at 300 W each. So they draw 300 W / 12V = 25 A each! If all these devices are on at the same time, the total current will be about 55 A. And what power is the battery supplying? P = IV = (55A) x (12V) = 660 W, exactly equal to the total (10 + 50 + 300 + 300 = 660 W) of what is being consumed by the devices.

Problem: Let's put a few numbers to the household circuit example. Assume we have a 100 W light fixture, and a 300 W television plugged into one of the outlets. What current do they draw?

Solution: For the light fixture, I = P/V = 100 W / 120 V = .83 A. Note that the 100 W light has the same current as the 10 W dome light in the previous example. Although the current is the same, the light fixture consumes 10 times the power of the domelight since it operates at 10 times the voltage.

The television consumes 300 W, so I = 300 W / 120 V = 2.5 A. Again, notice how the 300 W car headlight draws 10 times the current of the 300 W television. It must, since it operates at ¹/₁₀ the voltage.

Why do the Lights Dim?

If the dome light is on when you start the car, you'll probably notice it dims just a bit. The main reason is that the battery has internal resistance. The voltage may be 12 V when no current is being drawn. But when current flows through the battery, there is a potential drop across the internal resistance and the voltage at the battery terminals will be less than 12V. But you must be draw quite a bit of extra current to notice the change. A typical internal resistance might be only .01W. Let's say you turn on the dome light, drawing .83 A. The internal potential drop in the battery would be V = I R = .83A x .01W = .0083V. You turn on the radio, creating an additional drop of 4.2A x .01W = .042 V. You won't notice it. But when you start your car, the starter motor pulls 50 A. Now the potential drop is 50 A x .01W = .5 V. So the voltage across the battery and all the devices has dropped to about 11.5 V and you will probably notice the change.

Here's another example with a slightly different cause. The fridge or the air conditioner kicks on and you notice the house lights dim. It is not the internal resistance of WAPA! You may have inadequate wiring. Both these devices draw quite a bit of current in the first second or so when they first start up. If the wiring in your house is not "large" enough (i.e. the cross sectional area is too small), it will have too much resistance. When a large current is present in the wire, there will be a significant voltage drop, leaving less voltage available to your lights. You will notice that they dim.