Download Apply Ohm`s Law

Contents
Introduction
3
Ohm’s law relationships
4
The Ohm’s law equation
5
Calculating circuit current
6
Calculating resistance
7
Current direction and voltage polarity
9
Summary
14
Answers
15
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
1
2
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
Introduction
Ohm's Law states the relationship between the voltage across a resistor, the
current through a resistor and resistance. Ohm’s law allows us to perform
calculations to determine any one of current, voltage, or resistance from the
other two.
Ohm’s Law is the most extensively used equation in electrical theory.
After completing this topic, you should be able to:

state the relationship between voltage and current from measured values
in a simple circuit

calculate the voltage, current or resistance in a circuit given any two of
these quantities

interpret and draw graphs to show relationships of voltage, current, and
resistance

explain the relationship between voltage, current and resistance.
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
3
Ohm’s law relationships
In an electrical circuit, there is a definite relationship between current,
voltage and resistance that was discovered by Georg Ohm. He expressed the
relationships in written form, which became known as Ohm’s law.
In a circuit with a constant resistance, any increase in the applied voltage
will cause a proportional increase in current. This means for example that:

doubling the voltage doubles the current,

halving the voltage halves the current,

quartering the voltage quarters the current, and so on.
This relationship is one of direct proportion and can be written as:
IE
Read this as ‘current is proportional to emf’
Now if we maintain a constant supply voltage and vary the circuit resistance,
the circuit current changes in inverse proportion. That is:

doubling the resistance halves the current,

halving the resistance doubles the current,

quartering the resistance increase current four times, and so on.
This relationship is one of inverse proportion and can be written as:
I 
1
R
Read this as ‘current is inversely proportional to resistance’
4
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
The Ohm’s law equation
Ohm’s Law states that the current flowing through a resistance is:

directly proportional to the potential difference between them

inversely proportional to the resistance.
Ohm’s law may be written as:
V
R
where: V = voltage (volt)
R = resistance (ohm)
I = current (ampere)
I
Written as shown above, the Ohms Law equation expresses the current
resulting from a particular voltage (V) and resistance (R). But you will just
as often be given current (I) and resistance (R) and asked to find voltage (V).
Or you may be given current (I) and voltage (V) and asked to find resistance
(R).
Transposing to find R
Start with the basic equation:
I
V
R
Multiply both sides of the equation by R:
R I 
V
R
R
The letter R cancels on right hand side of the equation giving:
I  R V
Divide both sides by I:
R I V

I
I
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
5
The letter I cancels on left hand side of equation giving:
R
V
I
Transposing to find V
Start with the basic equation:
I
V
R
Multiply both sides of the equation by R:
IR 
V
R
R
Cancel Rs on right hand side:
I  R V
Usually it is expressed as:
V  IR
Summary
We have three forms for the Ohm's Law relation:
V
R
V
R
I
V  IR
I
Note that in any of these forms, the voltage (V) may also be an emf (E).
Calculating circuit current
Let's use the Ohm's Law equation to calculate current from voltage and
resistance. You may need to do this for example before you connect a
circuit, to check that the current will remain within safe limits.
Example 1
Determine the current in a 5  resistor when 12 V is applied.
6
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
Given R  5 
V  12 V
I ?
V
R
12

5
 2.4 A
I
Note: Always express answer as a decimal, not a fraction.
Example 2
If the voltage in Example 2 is reduced to 8 V, find the new current value.
Given R  5 
V 8V
I ?
V
R
8

5
 1.6 A
I
Calculating resistance
Example 3
A current of 6 A flows in a 10  resistor when connected to a 60 V supply.
What resistance will reduce the circuit current to 5 A?
Given V  60 V
I 5A
R?
V
I
60

5
 12 
R
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
7
Example 4
A variable resistor can have its resistance varied to control the current in
a circuit with a 120 V supply. If the current is to be varied from 25 A to 8 A,
what must be the variation in resistance in the variable resistor?
Given V  120 V
I max  25 A or I1  25 A
I min  8 A or I 2  8 A
R  ? (variation)
V
R1 
I1
120
25
 4.8 
V
R2 
I2

120
8
 15 

Therefore the variation in resistance of the variable resistor is from 4.8  to
15 .
If you have Hampson: Read the ‘Ohm’s Law section on pages 25 to 27,
including the calculations.
If you have Jenneson, refer to Section 2.8, ‘Ohm’s Law’ on page 34 for a
brief summary.
8
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
Current direction and voltage polarity
Current has a direction, which is often shown with an arrow. This is the
direction of the conventional current. Conventional current flows from the
positive terminal of the source of emf, through the circuit to the negative
terminal.
Every voltage or emf also has a direction, or polarity, which is indicated
using + and – signs on the component. The + sign indicates the end which is
at the higher potential (electrical pressure), and the – sign indicates the end
that is at the lower pressure.
The diagram below shows the current direction and polarities for a simple
circuit.
Figure 1: Current direction and voltage polarity
Note these points while looking at this circuit:

The source of emf is a battery, with the positive terminal at the top.
(We know this even without the signs, because the longer plate is the
positive one).

This emf causes the current to flow around the circuit in a clockwise
direction.

When the current encounters a resistor, it’s like a narrowing of a
water pipe – the pressure drops as we pass through the narrow pipe.
Likewise, the voltage drops as we pass through the length of the
resistor. This is why we often refer to the voltages across resistors as
a ‘voltage drop’.
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
9

The magnitude of the voltage drop across each resistor is given by
Ohm’s Law (V=IR).

Note that for a resistor, the end where the current enters will always
be at a higher electrical potential. It’s like water flowing downhill,
from higher to lower ‘gravitational potential’. Figure 2 below
illustrates this polarity.
Figure 2: Voltage polarity for a resistor
10
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
Activity 1
1
What is the relationship between voltage, current and resistance in a dc circuit?
_____________________________________________________________________
2
A circuit with a resistance of 2  has 10 V applied to it. Calculate the current flowing.
_____________________________________________________________________
3
If the voltage applied to a circuit is halved with the resistance remaining the same,
what happens to the current?
_____________________________________________________________________
4
If the resistance of a circuit is quartered (decreased by a factor of 4), with the applied
voltage remaining constant, what happens to the current?
_____________________________________________________________________
5
A variable resistor is used to control current in a circuit. If the resistance is varied from
15  to 45  and the supply voltage is 150 V, what variation in current can be
obtained?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Check your answers with those given at the end of the section.
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
11
Check your progress
1
Using Ohm’s law, fill in the blanks in the table below.
Voltage (V) volt
Current (I) ampere
30 V
12 V
3 k
40 m A
600 
4.8 m A
2.2 
330  A
12 M 
20 V
10 V
2
Resistance (R) ohm
10 A
Calculate the resistance of the lamp in the following circuit.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3
A 24  heating element requires a current of 10 A to produce its specified heat output.
Calculate the required supply voltage for this heater.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
12
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
4
Calculate the resistance of a resistor that takes 100 mA when connected to a 10 V
battery.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
5
Calculate the voltage across a 4.7 k resistor that has 3.5 A passing through it.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Check your answers with those given at the end of the section.
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
13
Summary

Ohm’s law states that the current in any circuit, or part of a circuit, is
directly proportional to the voltage and inversely proportional to the
resistance, that is:
I

V
R
The three equations obtainable from Ohm’s Law and its transpositions
are:
V
R
V  IR
I
R
14
V
I
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
Answers
Activity 1
1 Ohm's law I 
V
R
2
V
R
10

2
5A
I
3
The current is halved.
4
The current is increased by a factor of 4 that is, quadrupled.
5 At minimum resistance, R = 15 Ω and so
V
R
150

15
 10 A
I
At maximum resistance R = 45 Ω and so
V
R
150

45
 3.33 A
I
Therefore the current variation is 3.33 to 10 A.
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612
15
Check your progress
1
16
Voltage (V) volt
Current (I) ampere
Resistance (R) ohm
30 V
0.01
3 k
24
40 m A
600 
0.0106
4.8 m A
2.2 
12 V
330  A
36 364 
20 V
1.67× 10–6
12 M 
10 V
10 A
1
2
1200 
3
240 V
4
100 
5
16 450 V
EEE042A: 3 Apply Ohm's Law
 NSW DET 2017 2006/060/05/2017 LRR 3612