Electrical principles Ohm’s Law

•Describe how V, I, and R are related •Express I as a function of V and R•Express V as a function of I and R•Express R as a function of V and I •Show graphically that I and V directly proportional•Show graphically that I and R inversely proportional

Why can a bird sit on the power line?

Why can a bird sit on the power line?

• When does the current flow? If there are voltage or potential difference, then

the current starts to flow from high voltage to low voltage. But when a small bird sits on the power line, both feet are on the same voltage line!

Why can a bird sit on the power line?

• Let's say the power line is very low, almost touching the ground, and a chicken is trying to cross it. If one leg is on the ground and the other one is on the power line, then there are potential difference between these two legs.

Current (I)

• Current is the movement or flow of electrons along a conductor.

• When a battery is connected to a lamp with copper wires, the lamp illuminates. This is because as current flows through the filament of the globe (which has resistance), the filament becomes hot. The heating of the filament radiates light.

• The unit of measurement of current is the ampere (or amp).

Voltage (V)• Voltage is the term used to describe electrical pressure or

electromotive force (EMF).• A battery can create and store voltage or electrical pressure. • A battery has a build up of negative charge at one terminal and

positive charge at the other. These charges want to balance out, so there is an electrical force, or strain, between them.

• When a circuit is connected between the terminals of a battery, the electrical pressure (voltage) from the battery forces electrons to flow from the negative terminal to the positive terminal.

• The unit of measurement for voltage is the volt.• If 9V is marked on an electrical globe or other component, this

means that the component is designed to operate on nine volts of electrical pressure (voltage).

Resistance (R)• The filament of the globe contains resistance.• In an electrical circuit, resistance means opposition to

current flow. • The amount of resistance is directly related to how easily

atoms of specific materials give up electrons. Conductors have low resistance and insulators have high resistance.

• In an electrical circuit, components such as globes or appliances such as toasters provide resistance to current flow. All electrical components and circuits, including the wire, have resistance that will cause opposition to current flow.

• The unit for measurement of resistance is the ohm.• A device or component that is marked 10Ω will contain

10 ohms of resistance.

Quantity Symbol Unit Abbreviation Meaning

current I ampere A Flow of electrons

voltage V volt V Electrical pressure

resistance Ω ohm R Opposition to current flow

power P watt W Power dissipated

.

.

Review of V, I, and R

Voltage is

Current is

Resistance is

the amount of energy per charge available to move electrons from one point to another in a circuit measured in volts

the rate of charge flow and is measured in amperes

the opposition to current and is measured in ohms.

Quiz (V,R,I)1. Electrical current is defined as

a. Free electronsb. The rate of flow of free electronsc. The energy required to move electronsd. The charge on free electrons

2. Electrical voltage is defined asa. Opposition to the currentb. Is the movement or flow of electrons along a conductorc. the amount of energy per charge available to move

electrons from one point to another in a circuit measured in volts

3. The unit of Resistance is a. Voltb. Amperec. Ohm

4. The difference in potential energy in electrical terms is called .

a. Voltageb. Currentc. Resistance

Electrical basics• One way to help understand how current, voltage and resistance work is to

use an analogy. This means using something you already know and understand to help explain something new.

• The diagrams show how water can be a useful analogy to help understand electricity.

Summary

• Water pressure stored in the tank is similar to voltage (electrical pressure) stored in a battery.

• The flow of water through a pipe is similar to the flow of current through a wire.

• The path the water flows along causes a restriction to flow.

• The path the current flows through has a certain amount of resistance.

The following table lists the prefixes you are likely to use.

Prefix Symbol Meaning Value Factor

nano n 1,000,000,000th 0.000,000,001 10-9

micro u 1,000,000th 0.000,001 10-6

milli m 1,000th 0.001 10-3

centi* c 100th 0.01 10-2

deci* d 10th 0.1 10-1

kilo k 1,000 x 1,000 103

mega M 1,000,000 x 1,000,000 106

giga G 1,000,000,000 x 1,000,000,000 109

The first five prefixes are submultiples, ie they are smaller in value than the basic unit. The remaining prefixes are multiples , and they have larger values than the base unit.*centi and deci are only used in relation to metre, the unit of measure. Examples of submultiple and multiple:

• nano – 33nV equals 0.000000033 of a volt• micro – 33uV equals 0.000033 of a volt• milli – 33mV equals 0.033 of a volt• kilo – 33KV equals 33,000 volts• mega – 33MV equals 33,000,000 volts• giga – 33GV equals 33,000,000,000 volts.

Calculations with submultiple and multiple unitsWhen doing calculations with mixed quantities (any

combination of base, multiple or submutliple), all of the quantities should be converted to the base unit.

The conversion is done by moving the decimal point either left or right, based on the factor, as shown in the table.

To convert 33nV to volts: – 33 is multiplied by 0.000,000,001to get 0.000000033V

(decimal point moved nine places to the left on the number 33.0).

To convert 33mV to volts:– 33 is multiplied by 0.001 to get 0.033V (decimal point moved

three places to the left on the number 33.0).To convert 33GV to volts: – 33 is multiplied by 1,000,000,000 to get 33,000,000,000V

(decimal point moved nine places to the right on the number 33.0).

The conversion rule is:

submultiple to a base – move the decimal point to the left

multiple to a base – move the decimal point to the right.

When reading the value displayed on an electrical meter (particularly a multimeter), the value shown on the meter could be a base, multiple or submutliple.

Ohm's Law• Voltage, current and resistance are present in all operational circuits

and a relationship exists between these three things. The relationship is named after the person who discovered it, George Ohm.

• Ohm's law states, 'Current flow in a circuit is directly proportional to the voltage across the circuit and inversely proportional to the resistance contained in the circuit, providing circuit conditions remain the same.’

• In other words: • if you increase the voltage (or electrical pressure) in a circuit then the

current (flow of electrons) will increase in direct proportion, eg if you double the voltage the current flow will double

• if you increase the resistance (the opposition to current flow) in a circuit then the current flow will decrease in direct proportion, eg if the resistance in a circuit doubles then current flow will halve.

The image below shows that increasing battery voltage from 6 volts to 9 volts

will cause the current flow to increase in direct proportion.

The following image shows that If the resistance of the circuit is increased from 3Ω to 6Ω

(doubled) then the current flow will decrease inversely, ie it will reduce by half.

Ohm’s LawCurrent

(A)Voltage

(V)Resistor

(Ω)8 24 34 12 32 6 3

14 42 30.5 1.5 3

• Ohm's law states, Current flow in a circuit is directly proportional to the voltage across the circuit

• Graph is linear • Slope of the graph is

resistance and in this case is 3Ω

Show that the voltage increased in the circuit three times its present

value the current will triple in value

R=3kΩ

V= 24V

=

Show that the voltage increased in the circuit four times its present value the current will quadrupled in value

R=3kΩ

V= 24V

Problem

• You measured voltage and current in this circuit. For some reason current dropped from 2A to 1A .

• What value of voltage the voltameter will show now?

100V

2A

1 A

???

50

Graph of Current versus Voltage

I (m

A)

V (V )

00

2 4

4

6 8

8

10

12

14

16

A student takes data for a resistor and fits the straight line shown to the data. What is the resistance and the conductance of the resistor?

The slope represents the conductance.

14.8 mA - 0 mA1.48 mS

10.0 V - 0 VG

The reciprocal of the conductance is the resistance:

1 1 676 Ω

1.48 mSR

G

Your turn

Notice that the plot of current versus voltage for a fixed resistor is a line with a positive slope. What is the resistance indicated by the graph?

2.7 k

What is its conductance?

Voltage (V )

Cur

rent

(m

A)

0 10 20 300

2 .0

4 .0

6 .0

8 .0

10

G=5.6/15=0.37ms

R=1/G

Ohm’s Law

• Ohm's law states, Current flow in a circuit is inversely proportional to the resistance contained in the circuit

• Graph is a hyperbola

Voltage (V)

Current(A)

Resistor(Ω)

40 4 1040 10 440 2 2040 1 4040 40 1

To help you remember the formula, draw an Ohm's law triangle. Then, place your thumb over the unit you wish

to determine. The appropriate formula is shown as follows:

• If you cover V for voltage then the formula is IR

V = I x R• If you cover I for current then the formula

is V over RI = V / R• If you cover R for resistance then the

formula is V over IR = V / I• If any two values in a circuit are known,

the third value can be calculated.

The Ohm’s Law triangular

Ohm's law examplesSimple circuit.

1. What voltage would be measured on the voltmeter (V) if the resistor (R) has a value of 50Ω and has a current flow reading on the ammeter (A) of 0.5A?

V = IRV = 0.5 x 50V = 25 V

2. What would be the current flow (I) measured on the ammeter (A) in the circuit if 24V is applied to the resistance (R) of 120Ω?

I = V/R

I = 24/120I = 0.2 A or 200 mA

Ohm's law examplesSimple circuit.

3. What would be the resistance value (R) if a current flow of 1.5A is recorded on the ammeter (A) and voltage of 18V on the voltmeter (V)?R = V/IR = 18/1.5R = 12 Ω

4. How much current will be recorded on the ammeter (A) if the resistance (R) is 3kΩ (3000 ohms) and the applied voltage (V) is 12V? I = V/R

R is a multiple (k = 1,000) and must be converted to a baseR = 3kΩ = 3 x 1,000 = 3000ΩI = 12/3000I = 0.004 A or 4mA

1. Ohm's law describes how current is related to voltage and resistance.

1.True 2.False

2. The ampere is the unit of resistance. 1.False 2.True

3. The formula for finding resistance when current and voltage are known is R = I/V.

1.True 2.False

4. The formula for finding voltage when resistance and current are known is V = I/R.

1.True 2.False

Application of Ohm’s law

The resistor is green-blue brown-gold. What should the ammeter read?

26.8 mA

P o w er S u p p ly

+15 V- + - +5 V 2 A

D C A m m e te r

+-

G n d

V A

1. If the voltage is 12 V and the resistance in the wire is 3 Ω, what is the current in the circuit?

2. If you connect a wire with 18 Ω of resistance to a batter, and measure the current to be 10 A, what is the voltage of the battery?

3. What will happen to the current, if the resistance increases?

4. What would happen to the current in the circuit, if the voltage increases?

5. If the current equals to 14 A and the resistance is 3 Ω, what is the voltage of the battery?

6. If you connect a 7 V battery to a wire and measure the current to be 2 A, what is the resistance of that wire?

7. What is the resistance in the circuit that is connected to a 63 V battery, and is measured to have a current of 9 A.