1) Electromotive force [Emf (E)]

• The maximum amount of work done per unit charge which a cell
can produce.
W
• E = max
Q
• It is measured with a voltmeter when no current is flowing in the
circuit.
• The emf of a cell cannot change
• Unit: Volts (V)
2) Potential difference (V)
• The work done per unit positive charge.
W
• V =
Q
• The potential difference measured across the terminals of a
battery when a current is flowing through the battery is called
the terminal potential difference
• Unit: Volts (V)
• A Voltmeter is used to measure the potential difference of given
element (conductor, battery or resistor) is ALWAYS connected in
parallel for the element of interest.
 Electric current (I)
• The rate of flow of charge.
Q
• I=
∆t
• Measured in Ampere (A)
 Conventional current
• It is regarded as the flow of positive charges in a
conductor from the positive terminal of a source
through the circuit to the negative terminal of the
source.
• Ammeter is used to measure the current through
an element of interest (conductor, battery or
resistor) and is ALWAYS connected in series
• Resistance is defined to have a current inversely
proportional to it.
• A conductor has a resistance of one ohm if a current of
one ampere passes through when a potential difference
of one volt is maintained between it ends.
V
• R=
I
• Measured in ohms (Ω)
• Resistance is a material’s opposition to the flow of
electric charge ( or current)
 Factors influencing resistance of a conductor:
1. Type of material used.
2. Length of the conductor (R ∝ l)
1
3. Thickness of the conductor (R ∝ A
)
4. Temperature of the conductor (R ∝ T)
1) Type of material used
• Different materials have different resistance to the flow of charge
2) Length of the conductor
• Electric resistance (R) is directly proportional to the length of the
conductor
• The longer the conductor, the more collisions the charges will
make with its atoms
3) Thickness (cross-sectional area) of the conductor
• Electric resistance (R) is inversely proportional to the thickness (
cross sectional area) of the conductor
• The greater the diameter of the conductor, the more current the
conductor can carry
4) Temperature of the conductor
Electric resistance (R) is directly proportional to the temperature of
the conductor
According to the Kinetic Molecular Theory atoms vibrate more
rapidly at higher temperature, the charges moving through the
conductor (electrons) collide more frequently. Thus increasing the
resistance of the conductor
 A1 R1 R2 A2

V1 V2

V3

• Current remain the same. (I1=I2=constant)

• Divide the potential difference proportionally
(V3=V1+V2)
• The larger the resistance the greater the potential
difference
• The more resistors in series, the bigger the
resistance and the smaller the current
• Mathematically: 𝑅𝑠 = 𝑅1 + 𝑅2 + ⋯
 V3

A3 A2 R2

V2

A1 R1

V1

• Potential difference remains constant (V1=V2=V3)

• Divide the current inversely proportionally (I3=I1+I2)
• The larger the resistor, the smaller the current.
• The more resistors in parallel, the smaller the
resistance and the greater the current
1 1 1
• Mathematically: = + +…
𝑅𝑝 𝑅1 𝑅2
• The potential difference across a conductor is
directly proportional to the current in the
conductor at constant temperature.
𝑉
• In symbolic form: 𝑅 =
𝐼
 Ohmic and non-Ohmic materials
• An Ohmic conductor would have a linear
relationship between the current and the Potential
difference.
• Materials that obey Ohm’s law is said to be ohmic
 Ohmic Non-ohmic
• Metallic conductors Diodes, Transistors,
Semiconductors and light
bulbs
Investigation:

Potential difference (V)

SET UP Results
A
Switch B
Ammeter

A Material
tested

Rheostat
V
Current (A)
Voltmeter
• The gradient of the graph represents the resistance
• If the gradient is constant, A, than the material is
said to be ohmic
• If the gradient is not constant, B, than the material
is said to be non-ohmic
• The rate at which work is done.
𝐖
• Symbolic form: 𝐏 =
∆𝐭
• SI Unit: Watt (W)
W W Q
• Combining 1) P = , 2) V = and 3) I =
∆t Q ∆t
• Yields: 𝐏 = 𝐕𝐈
• Electrical power dissipated in a device is equal to
the product of the potential difference across the
device and the current flowing through it.
V
• Combining1) 𝐏 = 𝐕𝐈 and 2) R =
I
𝐕𝟐
• Yields: 𝐏 = and 𝐏 = 𝐈 𝟐 𝐑
𝐑
In the accompanying circuit the 24 V battery has no internal resistance and the
resistance of the ammeters are negligible.
24 V
A1

4Ω

6Ω
S1
A2
S2 12 Ω
V
1) What is the reading on Voltmeter V when both switches S1 and S2 are open?
2) Calculate the total resistance of the circuit when both S1 and S2 are closed.
3) Calculate the reading on the ammeters if both switches S1 and S2 are closed.
4) How would the energy produced by the battery, change when one of the
switches is open? Give a reason for your answer.
A circuit is set up as shown in the circuit
diagram. With switches S and K open,
Voltmeter V1 reads 18,0 V. Switch S and K S
K
are now closed. The ammeter A reads 3,0 A.
V1
1. Switch K is now also closed. Why does the 3Ω R V2
reading on A not change noticeably? A
2. Calculate the reading on voltmeter V2.
3. Calculate the resistance of resistor R. 3,6Ω
4. Calculate the power dissipated by the 3,6
Ω resistor
The diagram shows a circuit
containing four cells. When switch S is
closed, voltmeter V1 connected across
the battery reads 10,8 V.
V1
Calculate the : V2 3Ω 10,8 V A
6Ω
1. Reading on the ammeter. S
The switch S is now opened.
4Ω
2 Is the current through the ammeter
A greater than, less than or the
same as before? Explain your
answer.
3 Calculate the reading on voltmeter
V2 with Switch S open
In the accompanying circuit, a battery with an emf of 24 V is connected in
series with a resistor X and two identical light bulbs connected in parallel. The
battery has negligible internal resistance. Each bulb is marked: 6 V; 3 W.

6V;3W 6V;3W
X

1) Calculate the current which should flow in each bulb when it is used as it
specified voltage rating.
2) Calculate the resistance that x should have to ensure that each bulb
operates at its specified power rating.
3) Will the ammeter reading increase or decrease if:
3.1) Another identical light bulb is connected in parallel to the existing
two? Give a reason for your answer
3.2) Another resistor is connected in series with X? Give a reason for your
answer.
 Eskom is the main provider of electricity in South
Africa
 We are billed for the energy use per hour.
 The longer an appliance or device is used, the
more energy it converts and the more we pay.
 Energy consumption units at home is measured in
kilowatt hour (kWh).
 That is the use of 1 kilowatt of electricity for 1
hour
𝐖
 𝐏= → W = P∆t
∆𝐭
 Therefore the Cost (R) = cost per kWh×Power
rating in kilowatt ×time in hours
1) A heater is marked 2 000W/3 000W is switched on
for 4 hours. For the first hour, it is on the highest
setting and for the last 3 hours, it is on the lowest
setting.
1.1) How much energy does it transfer to the room in
kWh?
1.2 What is the cost of heating the room if electricity
cost 70c per kWh?
2) You are buying a new vacuum cleaner. There are
three models from which to choose. All are marked
220 V. One vacuum cleaner is marked 450 W while
the other two are marked 1200 W and 1600 W.
2.1) What do the marked values mean?
2.2) Which vacuum cleaner is likely to work most
effectively?
2.3) Which vacuum cleaner will be the cheapest to run?