Contents are appropriate for IGCSE Physics

1. Current, Resistance and
Electromotive Force

2. Electric Current
Electric current I is the flow of
charge Q through a cross-
section A in a unit of time t.
Q
I
t

1C
1 A
1 s

One ampere A is charge flowing at
the rate of one coulomb per second.
A
+
-
Wire
+Q
t

3. Example 1. The electric current in a
wire is 6 A. How much charge flows
past a given point in a time of 3 s?
I = 6 A
;
q
I q It
t
 
q = (6 A)(3 s) = 18 C

4. Exercise 1
1. What charge is delivered if:
a. a current of 10A flows for 25 seconds
b. a current of 250mA flows for 35 seconds
2. 4000 µC of charge flows past a point in 25
seconds. Calculate the current in the circuit.

5. Conventional Current
Electron flow: The direction
of e- flowing from – to +.
Conventional current:
The motion of +q from
+ to – has same effect.
We will be referring to conventional current in
most of the circuits (even if electron flow may
be the actual flow).
+
+
-
-
+ -
Electron
flow
+ -+ -
e-
Conventional flow
+

6. RESISTANCE
• Any conductor has some resistance that it
offers to the flow of current.
• Resistance is measured in Ohms (Ω)

7. Factors Affecting Resistance
1. The length L of the material. Longer
materials have greater resistance.
1 W
L
2 W
2L
2. The cross-sectional area A of the material.
Larger areas offer LESS resistance.
2 W
A
1 W
2A

8. Factors Affecting R (Cont.)
3. The temperature T of the material. The
higher temperatures usually result in
higher resistances.
4. The kind of material. Iron has more
electrical resistance than a similar copper
conductor.
Ro
R > Ro
Ri > Rc
Copper Iron
For semi-conductors, the higher the temperature, the lower the resistance.

9. Symbol of a resistor

11. Electromotive Force
A source of electromotive force (emf) is a
device that uses chemical, mechanical or
other energy to provide the potential
difference necessary for electric current.
Power lines Battery Wind generator
Potential Difference (p.d.) is the energy in a cell
used to push electrons round a circuit. It is
measured in Volt (V). It is also known as voltage.

12. Water Analogy to EMF
Low
pressure
PumpWater
High
pressure
ValveWater
Flow
Constriction
Source of
EMF
ResistorHigh
potential
Low
potential
Switch
E
R
I
+ -
The source of emf (pump) provides the voltage
(pressure) to force electrons (water) through
electric resistance (narrow constriction).

13. Ohm’s Law
Ohm’s law states that the current I through a
given conductor is directly proportional to the
potential difference V between its end points.
Ohm’s law allows us to define resistance R
and to write the following forms of the law:
' :Ohm s law I V
; ;
V V
I V IR R
R I
  

14. Example 2. When a 3-V battery is
connected to a light, a current of 6 mA
is observed. What is the resistance of
the light filament?
Source of
EMF
R
I
+ -
V = 3 V
6 mA
3.0 V
0.006 A
V
R
I
 
R = 500 W
The SI unit for electrical
resistance is the ohm, W:
1 V
1
1 A
W 

15. Exercise 2
1. Calculate the current through a circuit when a
p.d. of 12 V is applied across a 5Ω resistor.
2. What is the p.d. across a 3Ω resistor when
12mA of current passes through it?
3. How much current flows through a 13kΩ
resistor when it is connected to a 12V supply?

16. Resistivity of a Material
The resistivity r is a property of a material
that determines its electrical resistance R.
Recalling that R is directly proportional
to length L and inversely proportional
to area A, we may write:
or
L RA
R
A L
r r 
The unit of resistivity is the ohm-meter (Wm)

17. Example 3. What length L of copper wire is
required to produce a 4 mW resistor? Assume
the area of the wire is 7.85 x 10-7 m2 and that
the resistivity r of copper is 1.72 x 10-8 W.m .
A = 7.85 x 10-7 m2
L
R
A
r
-7 2
-8
(0.004 )(7.85 x 10 m )
1.72 x 10 m
RA
L
r
W
 
W
L = 0.183 mRequired length is:

18. RESISTIVITIES OF MATERIALS
Material Resistivity values (Ω.m)
Copper 1.72 x 10-8
Constantan 49 x 10-8
Manganin 44 x 10-8
Nichrome 100 x 10-8
Tungsten 55 x 10-8

19. Electric Power
Electric power P is the rate at which electric
energy is used, or work per unit of time.
It is measured in Watts (W)
V q
V
Power = voltage x current
(W) (V) (A)
P = VI I
Also, P = I2R

20. Using Ohm’s law, we can find electric power
from any two of the following parameters:
current I, voltage V, and resistance R.
Ohm’s law: V = IR
2
2
; ;
V
P VI P I R P
R
  

21. Electrical Energy
Electrical energy E is the amount of work
that can be done by an EMF. It is measured in
Joule (J).
E = Pt
Energy transformed (J) = power (W) x time (s)
Also, Energy = voltage x current x time
E = VIt

22. Example 5. A power tool is rated at 9 A
when used with a circuit that provides 120-V.
What power is used in operating this tool?
P = VI = (120 V)(9 A) P = 1080 W
Example 6. A 500-W heater draws a current
of 10 A. What is the resistance?
R = 5.00 W2
2 2
500 W
;
(10 A)
P
P I R R
I
  

23. Summary of Formulas
Q
I
t

1C
1 A
1 s

Electric
current:
; ;
V V
I V IR R
R I
  
Ohm’s Law
1 volt
Resistance: 1 ohm
1 ampere


24. Summary (Cont.)
or
L RA
R
A L
r r 
2
2
; ;
V
P VI P I R P
R
  
Resistivity of
materials:
Electric
Power P:

25. Exercise 3
1. How much power is developed in a battery of EMF 4.5V when a
current of 1.0A is passing through it.
2. A 23kΩ resistor is connected to a 6V EMF supply. Calculate;
a. the current flowing through the resistor.
b. the amount of charge passing through the resistor every 2
minutes.
c. the power dissipated by the EMF supply.
3. A bulb takes a current of 3A from a 12V battery
a. What is the power of the bulb?
b. How much energy is supplied in 10 minutes?
4. How much energy is transferred by a battery of EMF 4.5V when 1.0C
of charge passes through it for 2.5 minutes?

26. REVISION EXERCISE
1. When a kettle is plugged into the 230V mains, the current through its element is 10A.
a) What is the resistance of its element?
b) What is the power rating of the element?
c) If the element if made of copper. Copper has a resistivity of 1.72 x 10-8 W.m. If 2m
of copper wire is used, calculate its area.
d) How much electrical energy is used when the kettle is switched on for 21/2 hours?
2. If an electric heater takes a current of 4A when connected to a 230V supply, what is its
power?
3. If a light bulb has a power of 36W and resistance of 4Ω when connected to a power
supply.
a) How much current is flowing through the bulb?
b) Calculate the p.d. across the bulb
4. In 5 seconds, a hairdrier takes 10 000 joules of energy from the mains supply. What is
its power in
a) Watts
b) Kilowatts

27. Thanks!