Download Resistance and Resistivity

1 of 31
© Boardworks Ltd 2009
2 of 31
© Boardworks Ltd 2009
The effect of temperature on resistance
Resistance is a characteristic of all materials. Some materials
(e.g. air) have a high resistance. Other materials (e.g. gold)
have a very small resistance.
Electrical resistance is similar to friction, in that it is a resistance
to movement. Electrons drift slowly through a conductor when a
voltage is put across the ends. The metal’s atoms interfere with
the motion of the electrons, causing resistance.
electron
3 of 31
metal
atom
The higher the temperature,
the faster the metal atoms
vibrate, and the more likely
they are to impede electron
flow, hence increasing
resistance.
© Boardworks Ltd 2009
Ohm’s Law
Ohm’s Law states that:
The current in an ohmic conductor is proportional to
the voltage across it, provided that the temperature
and other physical conditions are kept constant.
We can write ‘voltage is proportional to
current’ in symbols as:
VI
If R is a constant:
V=R×I
R is the resistance, measured in ohms (Ω).
4 of 31
© Boardworks Ltd 2009
Finding resistance from a graph
Compare the equation for an ohmic conductor to the general
equation for a straight line:
V = RI
y = mx + c
V
If a graph is plotted with voltage
on the y axis and current on the
x axis, it can be seen that the
gradient (m) is the resistance.
The y intercept (c) is 0.
gradient = R
I
Voltage–current graphs are often drawn with the axes the other
way around. In this case, the gradient = 1/R and R = 1/gradient.
5 of 31
© Boardworks Ltd 2009
Plotting voltage–current graphs
6 of 31
© Boardworks Ltd 2009
How well do you understand graphs?
7 of 31
© Boardworks Ltd 2009
Which symbol and which graph?
8 of 31
© Boardworks Ltd 2009
Ohm’s Law summary
9 of 31
© Boardworks Ltd 2009
10 of 31
© Boardworks Ltd 2009
Equivalent resistance
R2
R1
R3
R4
R5
R6
RT
R7
When designing or analysing circuits, complex combinations of
resistors are common. To perform calculations, for example to
find a suitable fuse to protect the circuit, it is easier to use a
value for the total resistance of the circuit, RT.
RT can be called the equivalent resistance because it is the
single resistor that is equivalent to the complex combination.
11 of 31
© Boardworks Ltd 2009
Resistors in series
To work out the equivalent resistance of resistors in series,
the resistor values can just be added together:
10 Ω
20 Ω
15 Ω
equivalent resistance = 10 + 20 + 15
= 45 Ω
In general for a number of resistors, n:
RT = R1 + R2 + … + Rn
12 of 31
© Boardworks Ltd 2009
Resistors in parallel
To work out the equivalent resistance for resistors in parallel,
a more complex equation must be applied:
1
1
1
1
=
+
+ … +
RT
R1
R2
Rn
For example:
10 Ω
20 Ω
15 Ω
13 of 31
1
1
1
1
=
+
+
RT
10
20
15
1
6+3+4
=
RT
60
1 = 13
RT
60
RT
60
=
Ω = 4.62 Ω
13
© Boardworks Ltd 2009
Resistor combinations
14 of 31
© Boardworks Ltd 2009
15 of 31
© Boardworks Ltd 2009
What is resistivity?
Which of the four examples below has the largest resistance,
and which has the smallest?
The resistance depends
on the size and shape of
the material (its crosssectional area and length)
and the material itself.
copper
silver
silicon
plastic
16 of 31
The measure of how
much a particular material
opposes electron flow is
called the resistivity of
the material.
© Boardworks Ltd 2009
Introducing the resistivity equation
Resistivity is usually given the symbol r (the Greek letter rho).
Resistivity is calculated using the following equation:
resistance × cross-sectional area
resistivity =
length
RA
r=
L
The units of resistivity are ohm metres (Ωm).
Resistivity for a particular material varies with temperature,
so it is usually quoted for a particular temperature. This is
because resistivity depends on resistance, and resistance
varies with temperature.
17 of 31
© Boardworks Ltd 2009
Using the resistivity equation
18 of 31
© Boardworks Ltd 2009
Resistivity calculation
19 of 31
© Boardworks Ltd 2009
Effect of temperature on resistivity
20 of 31
© Boardworks Ltd 2009
Investigating the effect of temperature
21 of 31
© Boardworks Ltd 2009
Resistivity of different materials
22 of 31
© Boardworks Ltd 2009
23 of 31
© Boardworks Ltd 2009
E.m.f. and internal resistance
24 of 31
© Boardworks Ltd 2009
Using the e.m.f. equations
25 of 31
© Boardworks Ltd 2009
Finding e.m.f. and internal resistance
26 of 31
© Boardworks Ltd 2009
E.m.f. summary
27 of 31
© Boardworks Ltd 2009
28 of 31
© Boardworks Ltd 2009
Glossary
29 of 31
© Boardworks Ltd 2009
What’s the keyword?
30 of 31
© Boardworks Ltd 2009
Multiple-choice quiz
31 of 31
© Boardworks Ltd 2009