Back To Basics

There is a definite relationship between the three primary electrical characteristics: current, voltage and resistance. A German mathematician, George Simon Ohm, formulated this relationship in the 19th century. His law (Ohm’s Law) stated that current is directly proportional to voltage and inversely proportional to resistance. The following formula was derived from that law:

Current = Voltage/Resistance or I = E/R

Current (I) in amps: Voltage (E) in volts: Resistance (R) in ohms

Figure 7. Ohm’s Law

Ohm’s Law is the basic formula used in all AC and DC electrical circuits. So if you know two of the three characteristics, you can calculate the third one.

Electrical designers use it to determine how much voltage is required for a certain load, like a motor, a computer, or even a house full of appliances.

DC Circuits

We can use a simple DC circuit here to demonstrate Ohm’s Law. Before we do any calculations, however, let’s briefly discuss the symbols that will be used in our circuit diagrams.

Voltage Symbol : The terminals of a battery are symbolically indicated on an electrical drawing by one or more pairs of lines. The longer line represents the positive terminal, and the shorter line the negative terminal.

Figure 8. Voltage Symbol (Battery)

Resistance Symbol : Resistance is represented in one of two ways: either an open rectangle or a zigzag line. Resistance in a circuit can take the form of many different components from light bulbs to motors. Most of these components have their own unique symbols. For now, we will use the zigzag line symbol to represent the loads.

Figure 9. Resistance Symbol (Resistor)

Series Circuit

Using the simple circuit shown, assume that the voltage supplied is 12 volts, and the resistor provides six ohms of resistance. To determine the current, use the following formula.

Current (amps) = Voltage (volts)/Resistance (ohms)

Figure 10. Formula for Current

Another example of a simple DC circuit is a flashlight. Batteries in the flashlight provide the DC voltage source, the inside of the battery case usually acts as the conductor, and the lamp bulb is the load.

Figure 11. A Simple DC Circuit

The flashlight has an ON and OFF switch which controls the flow of electricity. Because there must always be a complete path for current to flow, the switch stops the flow when it is in the OFF position. Why? Because the circuit is open when the switch is OFF. When the switch is ON, the circuit is complete and current flows, lighting the bulb.

The simple circuits above are called Series Circuits, which means all loads are connected one after another in a series. If a conductor or a load is broken, it opens the circuit. This condition does not allow the current to complete the circuit and makes the entire circuit dead.

A good example of this is the old design for holiday lights. If one bulb was burned out, the entire string would not light.

Figure 12. Series Circuit

Take a look at the next series circuit. The voltage is unknown, but can be calculated using Ohm’s Law, E = IR. The current (I) is four amps as shown, but the resistance has to be calculated. In a series circuit, when more than one resistance is in the circuit, the resistances are added together to get the total resistance (RT). The R_T is 12 ohms. Given these two values and Ohm’s Law, the voltage is 48 volts.

Figure 13. Formula for Voltage

Now is a good time to talk about how current and voltage behave in a series circuit. The current value is the same in every part of the circuit. An Ammeter can verify this.

Voltage, on the other hand, does not remain constant throughout the circuit. Voltage values can be measured across each resistor or load. This is called the Voltage Drop. The total voltage (V_T) is equal to the sum of all the voltage drops in that circuit. A Voltmeter can verify this. The formula is:

(V_T) = V₁ + V₂ + V₃ …

Parallel Circuits

In Parallel Circuits, the loads are connected across the power line to form branches. The loads operate independently of each other, and therefore a break in any one branch does not prevent the line voltage from being applied to the remaining branches. The result is that one path (branch) can be open with the load not receiving current without the other loads being affected, as in the newer strings of holiday lights.

Current has a number of paths to follow. If all paths are available, the current divides itself between the branches back to the source. If a path is open, the current divides between the remaining available paths and goes back to the source.

Parallel circuits are used in the majority of industrial, commercial and residential applications of electricity.

The next two circuit illustrations show three resistors in parallel. The only difference between the two circuits is the resistor values. To use Ohm’s Law to solve the equations, you need to know how resistance, current and voltage behave in parallel circuits.

Figure 14. Parallel Circuit

The total resistance (R T ) of a parallel circuit decreases as more branches are added. The total resistance of a parallel circuit is always less than the resistance of any of its branches and is therefore less than the value of the lowest resistance in the circuit. To determine total resistance (R_T) two different formulas are used:

Resistors with Equal Values : This R_T is determined by dividing the value of one of the resistors by the total number of resistors in the circuit. Using this formula, the total resistance for the first circuit is calculated to be four ohms.

Figure 15. Resistors with Equal Value

Resistors with Unequal Values : Calculating R_T is more complicated and is shown below:

As a point of interest, the R_T for this circuit is 1.09W.

Figure 16. Resistors with Unequal Value

To determine current, you need to find the total current, which is the sum of all currents in all the branches. The following simple formula represents the total current (I_T), and the illustration offers a demonstration.

Figure 17. Total Current Formula

To determine the individual branch currents, it is necessary to know whether or not all the resistors have the same value.

Current with Equal Resistor Values : The current divides equally. Divide the total current by the total number of branch resistors to determine the current flowing through each branch. The following illustration and calculation demonstrate this procedure.

Figure 18. Current with Equal Resistors

Current with Unequal Resistor Values : The current is greater through the branch with the least resistance.

Parallel circuit voltage is easy to determine because it is the same across each resistor and/or load. The illustration shows a parallel circuit with voltmeters indicating the voltage across each resistor to be the same as the source battery.

Figure 19. Parallel Circuit Voltage