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3.1A Ohm's
Law
(and a mention of other units dealt with in other sections)
Questions to be answered: What is Ohm's
Law? How do you do calculations using Ohm/s Law? How do you construct and
use a circuit to investigate Ohm's Law? i.e. how to investigate the
variation of current in a circuit when the p.d. ('voltage') is varied.
Ohm's law states that the current (I
in A) passing through a
conductor between two points, is directly proportional to the voltage (potential
difference, p.d. in V) across the
two points in a circuit, and, inversely proportional to the resistance (in ohms,
Ω).
It involves a most fundamental equation
you need to know for electricity calculations.
This can be expressed mathematically as:
I
= V / R
rearrangements:
V = IR
and
R = V/I
(better than using formula triangle!)
I = current in amperes, amps,
A; a measure of the rate of flow of electric charge.
V = potential difference, p.d., volts,
V; a measure of the potential energy given to the electric charge
flowing.
The potential difference in a circuit
is the energy transferred per coulomb of electric charge that
flows between two points in an electric circuit.
The coulomb (C) is the
unit of electric charge (see
Q = It
equation notes). LINK
The energy transferred is
calculated from the p.d. and the quantity of electric charge (Q)
moved by the p.d. in V (see
E = QV
equation notes).. LINK
R = resistance of the wire, ohms,
Ω; a measure of the ability of a conductor to inhibit the
flow of charge.
The greater the resistance of a
resistor, the more it resists and slows down the flow of electricity.
Ohm's law means that the R in this equation
is a constant, independent of the size of the electrical current flowing.
The law correctly applies to so-called ohmic
conductors, where the current flowing is directly proportional to the
applied potential difference, but some resistors don't obey this law e.g. the heated filament of a
light bulb.
The basic circuit in the context of investigating Ohm's law.
3.1B A simple
experiment to measure the resistance of a single component with multiple
voltage-current readings
If you set up circuit 31 (right diagram) you can measure the
resistance of the fixed resistor [R].
By varying the voltage from the power supply using the
variable
resistor you can readily get lots of pairs of readings of p.d. (V) and current
(A).
Then use Ohm's Law equation
R = V/I to calculate the value of
the fixed resistance - examples of calculations below.
You can then average the values of R calculated for a more
reliable result.
This is the basic set-up to investigate
the current-voltage characteristics of any component R.
A voltmeter is always wired in parallel with the
resistor.
Examples of calculations using Ohm's
Law equation
Q1 When a p.d. of 4.5 V
is applied across a resistor, a current of 0.5 A flows.
What is the resistance of the device?
ANSWERS
Q2 A resistance has a
value of 50 ohms.
What p.d. must be applied across it
to cause a current of 5.0 A to flow through it?
ANSWERS
Q3
A p.d. of 240 volts is applied across a heating element resistor of 30 ohms.
How much current flows through the
heater?
ANSWERS
Q4
Three 1.5 volt batteries were wired in series with three bulbs.
If the ammeter measured a current of
0.50 A, what is the resistance of each bulb?
ANSWERS
3.1C
Investigating the
current - voltage
characteristics of a wire
This is an Ohm's Law experiment
Circuit
31 shows you how to investigate how I varies with V for a resistance
The investigation is all about finding
out ...
... how does the current flowing
through a resistor vary with the potential difference across it?
The fixed resistor represents a
'component' in a circuit and must be at constant temperature
throughout the experiment (see later on
temperature
effect in a metal filament bulb).
In this case
a simple wire resistor is
wired in series with the power supply and ammeter.
A voltmeter is always wired in parallel with the
resistor or any other device being investigated.
The p.d. is measured across the fixed
resistance with the voltmeter,
However,
also wired in series, a variable resistor is added, so that you can
conveniently change the potential difference and thereby change the current
flowing through the component.
This allows you to gather a whole series
of pairs of I and V readings, with which to plot suitable graphs - in this
case of V versus I, but often done as I versus V.
Using the variable resistor, you
gradually increase the potential difference across the component, taking the
matching current reading e.g. increasing at 0.5 V at a time. Repeat each
reading twice and use the average.
You can then swap the battery terminals
and repeat all the readings.
If you plot the p.d. versus current, the
graph is linear if it obeys Ohm's Law - it is then called an 'ohmic
conductor'.
This I've represented by the graph
above on the right, and the gradient is equal to the resistance in
ohms.
This corresponds to the Ohm's Law
equation V = IR, so the gradient is R.
If the graph remains linear, the
resistance is remaining constant.
This graph does not represent the
readings taken after reversing the battery terminals.
However, it does show how to get
the value of a resistance by a graphical method.
Its a linear graph and the
phrase linear component may be used.
For components like a wire that doesn't
heat up, you should get a linear plot of p.d. (V) versus I (A) with a
gradient R (Ω). (right graph).
You should make sure that the wire
doesn't heat up too much - if it starts getting warm, immediately
disconnect the resistor ('switch off') and let it cool down.
If you plot I versus V the gradient is 1/R (the reciprocal of the
resistance), linear graph.
This graph shows what you get by
plotting all the data, including the I-V readings taken after reversing
the battery terminals.
The graph
(1)
is
constructed on a crosswire axis. The top right half is your first set of
results, you then reverse the terminals on the power supply and repeat the
experiment giving the bottom left part of the graph.
Note that
you will only get a linear
graph if the temperature of the wire remains constant.
When the current (A) is proportional
to the p.d (V) it is described as an
ohmic conductor
(obeys Ohm's Law!).
Using the circuit 31 you can test any
resistor or any other type of circuit component and the results are
discussed below starting with a summary of factors that affect resistance.
So,
the resistance of an ohmic conductor e.g. a circuit
component doesn't change no matter current is passed through - constant
gradient of 1/R for graph 1.
Current versus voltage graphs for different wire resistances.
These are the expected linear graphs for
a fixed resistor using circuit 31 above.
Thinking anti-clockwise on the
diagram, the different graph lines might depict a decreasing resistance
e.g. (i) a resistance wire getting shorter for the same diameter, or
(ii) the diameter getting larger for a fixed length of wire.
At a constant temperature the current flowing through an
ohmic conductor is directly proportional to the potential difference across
it - the equation is V = IR or
I = V/R.
However, this is only true, giving
a linear graph if the temperature doesn't
change.
Comments about variables in this
particular Ohm's Law experiment
Current is always determined by a
combination of the p.d. (V) and the resistance R (Ω).
The independent variable is
what we change or control in the experiment - in this case you can
consider it as the p.d. controlled by the variable resistor.
One convention is to plot the
independent variable on the x-axis, and the dependent variable on the
y-axis.
This
means the resistance R, is the reciprocal of the gradient - a bit more
awkward to calculate the resistance than from the V versus I graph plot,
where the gradient is the resistance.
Ohm's Law: I =
V / R.
The dependent variable is what
we are testing or measuring in the experiment, this is the current I
(A), which depends on the variable resistor setting, which in turn
controls the potential difference across the resistor.
The control variables are what
we keep the same during the experiment to make sure it’s a fair test
e.g. in this case the wire and temperature are kept
constant, should NOT be varied - don't change the wire or allow the wire
to heat up.
3.1D
Electrical resistance - experiments to
investigate the I-V characteristic of various resistances and the validity, or
otherwise, of Ohm's Law
What affects the resistance of a wire? Is resistance
constant?
and some characteristic current-voltage graphs (I-V plots)
explained in Parts 3.2 to 3.4 (via index)
The resistance of a circuit depends on
several factors:
(i) the thickness of the resistance
wire - for a single component resistor
(ii) the length of the resistance
wire - for a single component resistor
(iii) if more than one resistance,
are they wire in series or parallel?
(iv) the temperature of a component
that acts as a resistance
These are looked at further in Parts 3.2 to 3.4
(links below)
3.2
Investigating the resistance of a wire at constant temperature, varying
length and diameter
3.3
Investigating current - voltage characteristics of a metal filament lamp - graph explained
3.4
Investigating the
current - voltage characteristics of a diode - graph explained
Parts
3.2 to 3.4 describe and explain several examples
of I-V graphs - which can be investigated using circuit 31 (on the right)
The circuit diagram 31 on the right shows
how you can investigate the variation of current through a resistance (or
any component) when you vary the potential difference.
Current–potential difference graphs are used to show how the current through a component varies with the potential difference across it.
The resistance of some resistors/components does change
as the current and p.d. changes e.g. a diode or filament lamp.
INDEX of electricity
section 3 notes on current, voltage, resistance, energy & charge
transfer in circuits including Ohm's Law investigations
Keywords, phrases and learning objectives for Ohm's Law in electricity
Know how to explaining Ohm's Law and electrical resistance
and use the formula in calculations.
Be able to describe the circuit and method used to measure
the variation of current with p.d. (voltage) to calculate
resistance.
Be able to use and rearrange the formulae I = V/R V=IR R = V/I
to solve problem involving calculations
relating current, p.d. voltage and resistance for an ohmic conductor.
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