ELECTRIC CIRCUITS
4.2.2 Electric Current
Objective/s:
By the end of the lesson, the learner should be able to:
1.
2.
3.
4.
State that current is related to the flow of charge
Use and describe the use of an ammeter, both analogue and digital
State that current in metals is due to a flow of electrons
Show understanding that a current is a rate of flow of charge and recall and use the equation
I=Q/t
5. Distinguish between the direction of flow of electrons and conventional current
6. Know the difference between direct current (d.c.) and alternating current (a.c.)
4.2.3 Electromotive force and potential difference
1. Define electromotive force (e.m.f.) as the electrical work done by a source in moving a unit charge around a
complete circuit
2. Recall and use the equation for e.m.f.
E = W/ Q
3. Know that e.m.f. is measured in volts (V)
4. Recall and use the equation for p.d. V = W/ Q
5. Define potential difference (p.d.) as the work done by a unit charge passing through a component
6. Know that the p.d. between two points is measured in volts (V)
7. Describe the use of voltmeters (analogue and digital) with different ranges
4.2.4 Resistance
1 Recall and use the equation for resistance R = V/ I
2 Describe an experiment to determine resistance using a voltmeter and an ammeter and do the appropriate
calculations
3 State, qualitatively, the relationship of the resistance of a metallic wire to its length and to its cross-sectional
area
4.2.5 Electrical energy and electrical power
1 Understand that electric circuits transfer energy from a source of electrical energy, such as an electrical cell or
mains supply, to the circuit components and then into the surroundings
2 Recall and use the equation for electrical power P = IV
3 Recall and use the equation for electrical energy E = IVt
4 Define the kilowatt-hour (kWh) and calculate the cost of using electrical appliances where the energy unit is the
kWh
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Standard Symbols

The diagram below shows the various circuit symbols that could be used in circuit diagrams.
You will be expected to know what each one is.
You are expected to be able to recognise and draw the above symbols
Diodes

In addition to the above, you should be able to recognise and draw the circuit symbol for a diode:
A diode is a component that only allows a current in one direction
(Note: Diodes are occasionally drawn without the horizontal line running through the middle of them)
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Current in a simple circuit
A cell (or a battery) can make electrons to move if there is conductor connecting its two ends.
Circuit symbol
The conducting path is a circuit.
Measuring current
Current is the rate of flow of charge.
The S.I. unit of current is the ampere (A)
Current in amperes =
In symbols, I =
𝑄
𝑡
𝑐ℎ𝑎𝑟𝑔𝑒 𝑖𝑛 𝑐𝑜𝑢𝑙𝑜𝑚𝑏𝑠
𝑡𝑖𝑚𝑒 𝑖𝑛 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
charge (Q) in coulombs (C)
Q
(1 A = 1 C/s)
𝑰 ×𝒕
Current (I) in amperes (A)
time (t) in seconds (s)
1 A = 1000mA
1 coulomb is the charge passing any point in a circuit when a steady current of 1 ampere flows for 1
second. ( 1C = 1 A.s)
An ammeter is used to measure current in a circuit. It is connected in series in the circuit.
Analogue
ammeter
Digital ammeter
Circuit symbol
The red (+) terminal is connected to the positive (+) terminal of the battery.
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Current direction
 Conventional current direction (from (+) round the circuit to (-) ) is equivalent to the transfer of
positive charge.
 Electrons being negatively charged are repelled by the negative charge hence pushed out of the
negative terminal of the battery.
 Mathematically, a transfer of positive charge is the same as a transfer of negative charge in the
opposite direction.
Series and parallel circuits
a) Series
The current is the same at all points in series circuit.
b) Parallel
The sum of the currents in the branches of a parallel circuit equals the
current entering or leaving the parallel circuit.
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QUESTIONS
1. Convert these currents into amperes: (a) 500mA
b) 2500mA
2. Convert these currents into millliamperes: (a) 2.0 A
(b) 0.1 A
3. What charge is delivered if:
(a) A current of 10A flows for 5 seconds?
(b) A current of 250mA flows for 40 seconds?
4. A charge of 0.01 C passes a point in a circuit every 0.2 s. What is the current flowing?
5. How long does it take for a charge of 30 C to pass a point in a circuit when a current of 0.8 A
flows?
6. How much charge will pass a point in a circuit when a current of 0.5 A flows for 1 minute?
7. The current in a circuit is 0.40 A.
Calculate the charge that passes a point in the circuit in a period of 15 s.
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8. Calculate the current that gives a charge flow of 150 C in a time of 30 s.
9. In a circuit, a charge of 50 C passes a point in 20 s. Calculate the current in the circuit.
10. A car battery is labelled ‘50 A h’. This means that it can supply a current of 50 A for one hour.
(a) For how long could the battery supply a continuous current of 200 A needed to start the car?
(b) Calculate the charge that flows past a point in the circuit in this time.
11. There is a current of 10 A through a lamp for 1.0 hour.
Calculate how much charge flows through the lamp in this time.
12. Calculate the current in a circuit when a charge of 180 C passes a point in a circuit in 2.0 minutes.
13. Calculate the number of protons that would have a charge of one coulomb.
(Proton charge = +1.6 × 10−19 C.)
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Electromotive Force




The Electromotive Force (EMF) is the Potential Difference (Voltage) of the power source in a
circuit.
Electromotive force e.m.f. is the electrical work done by a source in moving unit charge around a
complete circuit.
E = W/Q
The Electromotive Force (EMF) is measured in Volts (V).
The EMF is the voltage supplied by a power supply: 12 V in the above case

The EMF of a power supply (measured in volts, V) is the amount of energy (measured in joules, J)
supplied to each coulomb of charge passing through that power supply.
Potential difference
 The potential difference between two points in a circuit is the amount of energy transferred by each
unit of charge passing between those two points.
 Potential difference (p.d.) is defined as the work done by a unit of charge passing through a
component.
 The potential difference (voltage) across a cell can be measured by connecting a voltmeter across
the terminals of the cell.
 V = W/Q
 The S.I. unit p.d. the volt (V).
Digital voltmeter
Analogue
voltmeter
Circuit symbol
If the pd cross a cell is 1 V, then 1 J of potential energy is given to each coulomb of charge.
Voltage in volts =
𝑒𝑛𝑒𝑟𝑔𝑦 𝑡𝑟𝑛𝑠𝑓𝑒𝑟𝑟𝑒𝑑 𝑖𝑛 𝑗𝑜𝑢𝑙𝑒𝑠
𝑐ℎ𝑎𝑟𝑔𝑒 𝑖𝑛 𝑐𝑜𝑢𝑙𝑜𝑚𝑏𝑠
E
1 V = 1 J/C
𝑉×𝑄
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 Electromotive force (E.M.F.) is the voltage cross the terminal of a cell in an open circuit.
 When current is being supplied, the p.d. drops because of energy wastage inside the cell.
 In terms of energy, e.m.f. is defined as the number of joules of chemical energy transferred to
electrical energy and heat when one coulomb of charge passes through the battery (or cell).
e.m.f. = terminal p.d. + ‘lost’ volts
𝐸 = 𝐼𝑅 + 𝐼𝑟
QUESTIONS:
1. A lamp is connected to a battery in a circuit and a current flow.
a. Calculate the p.d. across the lamp if 6 J of work are done when 2 C of charge pass through the
lamp.
b.
If the p.d. across the lamp is increased to 5 V calculate the energy transferred to the lamp when a
current of 2 A flows in the lamp for 5 seconds.
2. Calculate the p.d. across a lamp in an electric circuit when 8 J of work are done when a charge of 4
C passes through the lamp.
3. The p.d. across a lamp is 6 V.
How many joules of energy are transferred when a charge of 2 C passes through it?
4. The p.d. across a lamp is 6 V.
Find the work done when a current of 3 A flows in the lamp for 10 s.
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Voltages round a circuit
(a) Series
The voltage at the terminals of a battery equals the sum of the voltages across the devices in the
external circuit from one battery to the other.
V = V1 + V2 + V3
(b) Parallel
The voltages across devices in parallel in a circuit are equal.
V =V1 = V2 = V3
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Series Circuits

A series circuit consists of a string of two or more components, connected end to end:
Diagram showing two bulbs connected in series

In a series circuit the current is the same at all points.
The current is the same at all points in a series circuit
Potential Difference in Series

When several cells are connected together in series, their combined EMF is equal to the sum of
their individual EMFs.
The total EMF of these cells is equal to the sum of their individual EMFs

In a series circuit, the sum of potential differences across the components is equal to the total EMF
of the power supply.
In a series circuit the components share the EMF of the power supply
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Parallel Circuits

A parallel circuit consists of two or more components attached along separate branches of the
circuit.
Diagram showing two bulbs connected in parallel



The advantages of this kind of circuit are:
o The components can be individually controlled, using their own switches.
o If one component stops working the others will continue to function.
In a parallel circuit the current splits up – some of it going one way and the rest going the
other.
This means that the current in each branch will be smaller than the current from the power
supply.
Determining Current in Parallel

Because the current splits up, the sum of currents in each branch will equal the current from the
power supply.
In a parallel circuit the current splits up, dividing between the various branches of the circuit


Note that the current does not always split equally – often there will be more current in some
branches than in others.
The current in each branch will only be identical if the components along each branch are identical
(or at least have the same resistance).
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QUESTIONS
1. If the lamps are both the same in the figure below and if ammeter A1 reads 0.50 A, what do
ammeters A2, A3, A4 and A5 read?
2. Three voltmeters V, V1 and V2 are connected as in the figure below.
a) If V reads 18 V and V1 reads 12 V, what does V2 read?
b) If the ammeter A reads 0.5 A, how much electrical energy is changed to heat and light in lamp
L1 in one minute?
c) Copy the figure above and mark with a + the positive terminals of the ammeter and voltmeters
for correct connection.
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Resistance


Resistance is the opposition to flow of current.
o For a given potential difference:
The higher the resistance, the lower the current.
Potential difference, current and resistance are related by the following equation:
potential difference = current × resistance
V = I×R
V
I × R
Use the formula triangle to help you rearrange the equation

The unit of resistance is the ohm (Ω).
Determining Resistance

To find the resistance of a component, set up a circuit like the one shown below.
A circuit to determine the resistance of a component



The power supply should be set to a low EMF (voltage) to avoid heating the component – 1 or 2
volts is typically enough.
Measurements of the potential difference and current should then be taken from the voltmeter
and ammeter respectively.
Finally, these readings should be substituted into the following equation:
𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =
𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝑐𝑢𝑟𝑟𝑒𝑛𝑡
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QUESTIONS:
1. A potential difference of 20 V is required for a current of 0.5A to flow through a resistor. What is
its resistance?
2. A current of 0.01 A flows through a resistor of 1 kΩ . What is the potential difference across the
resistor?
3. How much current flows when a potential difference of 5 V is applied to a resistor of 10Ω?
4. Calculate the current in a lamp given that its resistance is 15 Ω and the potential difference across its
ends is 3.0 V.
5. Calculate the resistance of a lamp carrying a current of 0.40 A when connected to a 230 V supply.
6. In the figure, the reading on the ammeter is 2.4 A and the reading on the voltmeter is 6.0 V.
Calculate the resistance of the metallic conductor.
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Resistance of a Wire:

As electrons pass through a wire, they collide with the metal ions in the wire.
Electrons collide with ions, which resist their flow



The ions get in the way of the electrons, resisting their flow.
If the wire is longer, each electron will collide with more ions and so there will be more
resistance:
The longer a wire, the greater its resistance (the resistance of a wire is proportional to its
length).
If the wire is thicker (greater diameter), there is more space for the electrons and so more
electrons can flow:
The thicker a wire, the smaller its resistance, (the resistance of a wire is inversely
proportional to its cross-sectional area).
Current & Potential Difference


As the potential difference (voltage) across a component is increased, the current in the
component also increases.
The precise relationship between voltage and current can be different for different types of
components, which is shown by an IV graph:
I - V graphs for a resistor and a filament lamp
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 The I - V graph for a resistor is a straight line through the origin:
The current is proportional to the potential difference (Ohmic conductor)
 This is because the resistor has a constant resistance.
 For a lamp, the I - V graph is a curve (non-ohmic conductor):
The current increases at a proportionally slower rate than the potential difference.
 This is because:
o The current causes the filament in the lamp to heat up
o As the filament gets hot its resistance increases.
o This opposes the current, causing it to increase at a slower rate.
Resistors in Series & Parallel
Resistors in Series
When two or more components are connected in series:

The combined resistance of the components is equal to the sum of individual resistances.
When several components are connected in series, their combined resistance is equal to the sum of
their individual resistances
Resistors in Parallel
1
1
1
=
+
𝑅
𝑅1
𝑅2
𝑅=

𝑅1 𝑅2
𝑅1 + 𝑅2
=
𝑃𝑅𝑂𝐷𝑈𝐶𝑇
𝑆𝑈𝑀
When resistors are connected in parallel, the combined resistance decreases and is less than the
resistance of any of the individual components.
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
If two resistors of equal resistance are connected in parallel, then the combined resistance will
halve.
The above resistors will have a combined resistance of 2 Ω − half the value of each resistor
Worked example
A p.d. of 24 V from a battery is applied to the network of resistors in the figure below.
a) What is the combined resistance of the 6 Ω and 12 Ω resistors in parallel?
b) What is the current in the 8 Ω resistor?
c) What is the voltage across the parallel network?
d) What is the current in the 6 Ω resistor?
Solution
c) V = IR
a) Let R1 = resistance of 6 Ω and 12 Ω in
parallel
V =2X4
6 ×12
𝑅1 = 6+ 12 = 4 Ω
=8V
b) Let R = total resistance
d) 𝐼 =
4 + 8 = 12 Ω
𝑉
𝐼= 𝑅 ,
24
𝐼 = 12 = 2 𝐴
0
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𝑉
𝑅
𝐼=
8
6
= 1.33 A
QUESTIONS
1.
Calculate the charge which passes through a lamp when there is a current of 150 mA for 40 minutes.
2.
A generator produces a current of 40 A.
How long will it take for a total of 2000 C to flow through the output?
3.
In a lightning strike there is an average current of 30 kA, which lasts for 2000 μs.
Calculate the charge which is transferred in this process.
4. a) A lamp of resistance 15 Ω is connected to a battery of e.m.f. 4.5 V.
Calculate the current through the lamp.
b) Calculate the resistance of the filament of an electric fire which takes a current of 6.5 A when it
is connected across a mains supply of 230 V.
c) Calculate the voltage which is required to drive a current of 2.4 A through a wire of resistance 3.5 Ω.
5.
A battery of e.m.f. 6 V produces a steady current of 2.4 A for 10 minutes. Calculate:
a) the charge which it supplies
b) the energy that it transfers.
6.
Calculate the energy gained by an electron when it is accelerated through a potential difference of
50 kV. (Charge on the electron = 1.6 × 10−19 C.)
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7. Calculate the combined resistance of two 5 Ω resistors and a 10 Ω resistor connected in series.
8. Two 10 Ω resistors are connected in parallel. Calculate the total resistance.
9. Fig. 9.1 shows a circuit containing a battery, three resistors and an ammeter.
Fig.9.1
(a) (i) Write down the equation for the effective resistance Rp of two resistors of resistances R 1 and
R2 connected in parallel.
(ii) Use this equation to calculate the effective resistance of the two resistors in parallel in the Fig.
(b) A voltmeter is to be used to measure the potential difference across the resistors in parallel.
(i)
On Fig. 9.1, draw the voltmeter in position in the circuit, using the correct circuit symbol.
(ii) The ammeter reads 1.6 A. Calculate the reading on the voltmeter
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Electrical Energy

As electricity passes around a circuit, energy is transferred from the power source to the various
components (which may then transfer energy to the surroundings).
o As charge passes through the power supply, it is given energy.
o As it passes through each component, it loses some energy (in transferring that energy to
the component).
The current transfers electrical energy from the power source and to the components
Calculating Electrical Energy


The amount of electrical energy used by a component or appliance depends upon three things:
o The current
o The potential difference
o The amount of time the device is used for.
The energy transferred can be calculated from the equation:
Electrical energy transferred = current × potential difference × time
E = I×V×t
E
Where the unit of energy is the joule (J)
I × V × t
Electrical Power


Power is the rate of energy transfer (the amount of energy transferred per second).
The power of an electrical component (or appliance) is given by the equation:
Power = Current × potential difference
P = I×V

The unit of power is the watt (W), which is the same as a joule per second (J/s)
Energy transferred = power x time = potential difference x current x time
E=V×I×t
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P
I × V
Questions
1. a. What is the power of a lamp rated at 12 V 2 A?
b. How many joules of electrical energy are transferred per second by a 6 V 0.5 A lamp?
2. The largest number of 100 W lamps connected in parallel which can safely be run from a 230 V
supply with a 5 A fuse is
A. 2 B. 5
C. 11
D. 12
E. 0
3. What is the maximum power in kilowatts of the appliance(s) that can be connected safely to a 13 A
230 V mains socket?
4. Fig. below shows a circuit containing a battery of electromotive force (e.m.f.) 12 V and a heater of
resistance 6.0 Ω.
(a) State what is meant by electromotive force (e.m.f.).
...................................................................................................................................................
...............................................................................................................................................[1]
(b) (i) Calculate the current in the heater.
current = .............................................[2]
(ii) State the name of the particles that flow through the heater.
.......................................................................................................................................[1]
(iii) On the Fig., draw an arrow next to the heater symbol to show the direction of flow of these
particles through the heater. [1]
(c) Calculate the thermal energy produced in the heater in 10 minutes.
thermal energy = ........................................[2]
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