Theme 2: Energy and the Environment Background Material
This section contains background material on Ohm's Law. For additional background information, see Phase 1.

Ohm's Law

Resistors
In electronics, resistance is provided by a technological device called a "resistor."

Inside a fixed resistor Diagram from "Ultimate Visual Dictionary of Science," Stoddart 1998.

A resistor regulates the flow of electric current in a circuit. If a battery is attached to a closed circuit, a voltage differential is established. Resistors can control current from a battery by producing opposing voltages that increase with the current flow. When the power is switched on, current increases until the resistor voltages balance the battery voltage. This limits the current flow through the resistor. Resistance is measured in units called Ohms.

This effect may be used directly in electrical circuits. For example, a light-emitting-diode (LED) may require 3.6 volts to operate. If a 9-volt battery is used, the LED would quickly burn out. However, if the appropriate resistor is added to the circuit, the voltage over the LED will be lowered. Lowering the voltage will prevent the LED from being damaged or destroyed. The resistor lowers the voltage in the entire circuit.

Resistors get hot when they are working because they exert control by converting power to heat. They can only reduce the power of an electric signal, never increase it.

Ampere - unit of flow
The term ampere is the unit of electric current flow and is simply a measure of the rate at which electrons are flowing in a circuit. For example, a current flow of 2-Amps is flowing twice as fast as a flow of 1-Amp. A current flow of 4-Amps is flowing four times faster than a flow of 1-Amp.

Voltage - unit of pressure
The pressure behind the electrons affects their rate of flow or amperes. The pressure, called voltage, is the electric pressure applied to electrons to make them flow. The volt is the common name or unit used to measure the electric pressure.

A volt is a certain amount of electric pressure, or force, tending to cause any electrons present to flow in an electric current. For example, 4 volts produces four times the number of amperes that would result from 1 volt. 10 volts produces ten times the number of amperes compared to 1 volt.

Ohm's Law
In order to understand Ohm's Law, the following points should be reviewed:

• Current flow is measured in Amperes (A).
• Voltage is measured in volts (V).
• Resistance is measured in Ohms (O or Greek symbol "omega").
• Electric power is measured in Watts (W).

• Current flow is measured in Amperes (A) and is designated as I which stands for Intensity of flow.
• Voltage is measured in volts (V) and is designated with an E which represents the Electromotive Force of pressure of flow.
• Resistance is measured in Ohms (O or Greek symbol "omega") and is designated with the symbol R for resistance.
• Electric power is measured in Watts (W).

• Electric current flows from high electrical pressure to low electrical pressure.
• The greater the voltage, the greater the current flow. The more resistance, the less current flow through the circuit.

Ohm's Law is a simple equation that makes it easy to:

• calculate the number of Amperes in a circuit when the voltage and the resistance are known
• calculate how many volts pressure is needed to push a certain current through a known resistance
• calculate how many ohms of resistance will keep the current to a certain amperage in a circuit of known voltage

According to Ohm's Law, voltage and current are directly related - a change in voltage produces a change in amperage.

1. To calculate the resistance required, the following formula is used:

This formula can also be described as: Ohms = volts/Amps or with symbols: R = V/I

2. To calculate the number of volts required, the following formula is used:

This formula can also be described as: Volts = Amps X Ohms or with symbols: V = I X R

3. To calculate the amperage of current flow in a system, the following formula is used:

This formula can also be described as: Amps = volts/ohms or with symbols: I = V/R

Resistance
George Simon Ohm (1785 - 1854) was the first person to publish the results of experimentation on the resistance of wires of various sizes. Ohm constructed wires of many different lengths and thicknesses. Today, we simply call these devices resistors because all they do is resist the flow of current. Ohm applied a potential difference (voltage) across his wire resistors and measured the current through them. He discovered that, for each resistor, no matter what potential difference he applied, the resistance was the same.

Electrical resistance is another term for the friction of material to the flow of the current through it. Resistance is anything that causes an opposition to the flow of electricity in a circuit. To force current will generate heat in the conducting material.

Resistors are very important in circuits. They are used to control current or potential difference in a circuit. For example, if you connect an LED directly to a battery (cell) you will likely destroy the LED unless you have a resistor in the circuit to control the potential difference.

The unit measurement for resistance is called the Ohm and is indicated by the Greek letter Omega (O).

All materials have resistance, whether they carry current or not. The resistance of a material is always the same - unless it is physically altered. For example, if you stretch a wire, it will have more resistance.

Measuring Resistance
The easiest method to measure resistance is to measure the current delivered to the device and the voltage drop across it at that specific current. This is done by using an ammeter placed in series and a voltmeter placed in parallel with the resistor.

A voltage drop is the amount the voltage lowers when crossing a component from the negative side to the positive side in a series circuit. If you placed a voltmeter across a resistor, the voltage drop would be the amount of voltage you are reading.

Then the resistance (R) of the device may be found by dividing the voltage (V) by the ammeter reading (I). R = V/ I

Series Resistance
Whenever two or more resistors are connected in series, certain facts exist about the entire circuit.

Facts:
1. The maximum allowable current in the circuit is the smallest allowable current in any one part of the series circuit.

If any part of the circuit can only withstand two amperes of current, then the current (2 Amps) is the maximum allowable current for the entire circuit.

This is true even if other parts of the circuit are capable of withstanding a much higher current.

2. Current flow through the entire circuit will be the same in all parts of the circuit. In this example, the current flowing is 1 Amp.

3. The total resistance of a series circuit is equal to the sum of all resistances in series.

R_T = R1 + R2 + R3...
In this example, the R_T = 5 + 5 = 10 Ohms

4. The voltage applied to a series circuit is equal to the sum of the individual voltage drops around the circuit.

V = V1 +V2 +V3
V = (IR) 1 + (IR) 2
Total Voltage = (1 A x 5 W) + (1 A x 5 W)
= 5V + 5V = 10 V

Note: The current in the external circuit flows from the Negative terminal to the Positive terminal. This is the direction of the electron flow. However, the current actually flows from Positive battery terminal, through the resistor, and into the Negative battery terminal.

Parallel Circuits

Parallel circuits are very common in household wiring. Parallel circuits have more than one path (branch) for the current to follow.

Each branch connects across the main line. Therefore, all branches are in parallel.
In any parallel circuit, all branches get the same voltage.

Ohm's Law in Parallel Circuits
Keep all values of amps, volts, and Ohms referring to a specific part of the circuit. For example, a circuit in a house carries 110 volts. Allowing a current of 3 amps for a toaster, 1 amp for a table lamp, and 5 amps for an iron, the equivalent resistance can be calculated as follows:

Iron: R = V/I = 110 V / 5 A = 22 Ohms
Toaster: R= V/I = 110 V / 3 A = 36.7 Ohms
Lamp: R = V/I = 110 V / 1 A = 110 Ohms

Equivalent Resistance = Volts / Amps (total)
= 110 V / (5 + 3+ 1)
= 110 V / 9 Amps = 12.2 Ohms

In any parallel circuit, the equivalent resistance will be less than any of the branch resistances. Adding more parallel resistances to the branches causes the equivalent resistance in the circuit to decrease.

Parallel Circuits
1. In all parallel circuits, there is more than one current path or branch. All branches connect back to the main line.

2. The voltage over all branches is the same as the main-line voltage - all are equal.

V (main) = (IR) 1 = (IR) 2 = (IR) 3

IT = I1 + I2 + I3...

IT = (V/R) 1 + (V/R) 2
IT = (10 V / 10 W) + (10 V / 10 W)
IT = 1 A + 1 A = 2 Amps

Parallel Resistance
The Equivalent Resistance of all the branches combined is less than resistance of the smallest branch. The Equivalent Resistance of a Parallel circuit is calculated with the following formula:

1/R_E = 1/R1 + 1/R2 + 1/R3...

A circuit has three resistors (5 Ohm; 5 Ohm; 4 Ohm) in parallel. The Equivalent Resistance (R_E) can be calculated as follows:

1/R_E = 1/R1 + 1/R2 + 1/R3
1/R_E = 1/5 + 1/5 + 1/4

1/R_E = .2 + .2 + .25
1/R_E = 0.65
Rt = 1 /.65 = 1.54 Ohms

The Total Resistance of 1.54 Ohms is less than the resistance of the smallest branch (4 Ohms).

Note: Students should check that the total resistance for the iron, toaster, and lamp described earlier is in fact 12.2 Ohms.

Note: If there are only two resistors in parallel, the formula can be simplified as shown: R_E = (R1*R2)/(R1 + R2)