Current and Voltage
Introduction


Many scientists in the eighteenth century believed that there was only one type of mobile electrical charge: positive electricity. They proposed that materials became positively charged when electrical particles were added to them while materials having fewer electrical particles were negatively charged.



These scientists were correct in thinking that objects were charged by the movement of electrical charges. However modern experiments have shown that objects are generally charged by the movement of negatively charged electrons. The properties of conductors, insulators, and even semiconductors can be explained by considering the movement of electrons.

Charges on the move
Press the button in Fig.1 below to start the experiment. You should notice that when the ping-pong ball, coated with metallic paint, is touched against the negatively charged plate it begins shuttling to and fro between the charged plates.
Figure 1.   Direct current from charges on the move.
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Complete the following statements to describe the motion of the ball in Fig.1 above.

  • When touched momentarily against the negative plate the ball becomes charged. The ball is from the negative plate and towards the positive plate. On touching the positive plate it gives up its negative charge and becomes charged instead.
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Use the slider to alter the distance between the plates and note that the
current
The rate of flow of charge past any specific point in a circuit. The base unit of current is the Ampere.
current
shown on the ammeter changes.

What happens to the current measured by the ammeter when you increase the separation between the plates?
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The
unbalanced force
Unbalanced forces occur in situations where the force acting in one direction is greater than the force acting in the opposite direction.
unbalanced force
acting on the charged ball in Fig.1 causes it to shuttle backwards and forwards between the plates. The very sensitive ammeter in Fig.1 measures the rate at which the ball transfers small quantities of charge from one terminal of the power supply to the other across the gap.

Moving the plates closer together makes the ball shuttle more frequently between the plates and so the total quantity of charge transferred per second increases. This is shown as a higher reading on the ammeter.

Push the switch in the circuit in Fig.2 to connect the power supply and ammeter to a lamp.


Click on the figure below to interact with the model.

 Figure 2.  Creating a current.



Pushing the switch in Fig.2 means that the lamp lights up and the ammeter registers a current.

What size current (in mA) does the ammeter detect?
  •  mA
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From the shuttling ball experiment in Fig.1 we saw that when the ball transferred charges, the ammeter detected a current. In the circuit in Fig.2 we see that when we pushed the switch to connect the power supply, the ammeter again detected a current. From these two observations we can conclude that a current is a flow of individual charges from one terminal of a power supply to the other.

Charge and current
Quantities of charge are measured in coulombs (C). One
coulomb
The coulomb is the unit of charge. One coulomb is approximately equivalent to the charge carried by 6.25 × 1018 electrons.
coulomb
is approximately equivalent to the charge carried by 6.25 × 1018 electrons.

What is the approximate charge in coulombs carried by 1.25 × 1020 electrons
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Current is defined as the rate of flow of charge. This means that the size of a steady current is the quantity of charge flowing past a particular point in a circuit in 1 second. The base unit for current is the
ampere
The ampere is the base unit of electrical current.The precise definition of 1 ampere is stated in terms of the magnetic effect of a current passing through a conductor; however, as a working definition we can say that there is a current of 1 ampere in a circuit when 1 coulomb of charge passes any point in 1 second.
ampere
(A), often abbreviated to amp. The current in any particular part of a circuit is measured using an ammeter.

The precise definition of 1 ampere is stated in terms of the magnetic effect of a current passing through a conductor; however, as a working definition we can say that there is a current of 1 A in a circuit when 1 C of charge passes any point in 1 second. In symbols, the current in a circuit I is defined as:



where Q is the quantity of charge, in coulombs, moving between the ends of a conductor in a time of t seconds.

What is the current in a circuit where 24 coulombs of charge flow through a lamp in 30 seconds.
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The current in a heater is a steady 5 A. Calculate the quantity of charge passing through the heater's heating element in 2.5 minutes.
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Our definition states that a current is the flow of charge per second. A current of 5 A indicates that charge is flowing in a circuit at a rate of 5 coulombs per second (Cs−1). Therefore we can say that 5 A is equivalent to 5 coulombs per second (5 Cs−1). By rearranging the equation above we can also see that a charge of 500 C could be written as 500 amp seconds (500 As).

Current in a series circuit
When the switch is closed in the circuit in Fig.3 the ammeters show the currents before and after each of the components in the simple series circuit.

Click on the
voltage
The voltage across a component is the electrical energy transferred by 1 coulomb of charge passing through the component.
voltage
value above the battery in Fig.3 and enter a new value for the battery voltage in the range 0 to 20 V.


Click on the figure below to interact with the model.

 Figure 3.  Current in a series circuit.

Complete the following statements for the circuit in Fig.3 (to 1 d.p.).

  • When the battery voltage is 15 V the current between the components is  mA. The current shown on the ammeter between the battery and the buzzer is  mA. The current between the LED and the battery is  mA.
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When components are joined in series the current at all points in the
series circuit
Components are connected in series when the same electrical charges pass through both.
series circuit
is the same. This can be expressed mathematically as:



Any alteration to the supply voltage will alter the size of the current at all points in a series circuit.

Current in a parallel circuit
The circuit in Fig.4 shows a lamp and buzzer connected in parallel. Ammeters are used to measure the current at various parts of the circuit. When the switch is closed, two of the ammeters show the currents in the branches of the
parallel circuit
Components connected in parallel offer alternative paths for charges from a supply.
parallel circuit
. The other ammeter shows the total current supplied by the battery.

Click on the battery in Fig.4 and enter any value for the battery voltage in the range 0 to 20 V. Pay particular attention to the readings on the ammeters.


Click on the figure below to interact with the model.

 Figure 4.  Simple parallel circuit.



Complete the following statements for the circuit in Fig.4 (to 1 d.p.).

  • When the supply voltage is set at 15 V, the current in the buzzer is  mA. The current in the lamp is  mA. The total current taken from the battery is  mA.
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Compare the three current readings you have taken.

Which statement below describes the relationship between the three readings.
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Change the battery voltage and see if the relationship is still true.

You should have found that when components are joined in parallel, the total current taken from the battery is equal to the sum of the currents in the parallel branches.

This can be expressed mathematically as:



This equation can also be described by saying that the sum of the currents entering a junction in a circuit is equal to the sum of the currents leaving the junction. This is known as
Kirchhoff's First Law
The sum of the currents entering a junction in a circuit is always equal to the sum of the currents leaving it.
Kirchhoff's First Law
.

Kirchhoff's First Law
Kirchhoff's First Law is a consequence of the fact that there is no build-up of charge at any point in a simple circuit so charges must flow into and out of any junction in a circuit at the same rate.
Figure 5.   Using Kirchhoff's First Law.
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Use Kirchhoff's First Law to work out the current leaving the junction in Fig.5 above.
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Figure 6.   Using Kirchhoff's First Law.
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The unknown current in the diagram of Fig.6 above is …
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Voltage
When the switch in Fig.7 is held closed some chemical
energy
A system has energy when it has the capacity to do work. The scientific unit of energy is the joule.
energy
from the battery is converted into electrical energy in the form of moving charges.


Click on the figure below to interact with the model.

 Figure 7.  Producing sound.



Push the switch in Fig.7 to complete the circuit. As charges pass through the buzzer some of their electrical energy is converted into sound. Since energy is given out by the buzzer, the charges leaving the buzzer have less energy than those entering. This electrical energy difference across the buzzer is maintained by the battery. Each coulomb of charge moving from the high-energy side of the battery to the low-energy side carries a certain quantity of energy from the battery to the buzzer.

The voltage V across the buzzer is defined by the equation:



where W is the electrical energy transferred by Q coulombs of charge passing through the buzzer. With this definition we are able to describe the voltage as the energy transformed per coulomb. A 6 V battery will transfer 6 joules of energy to each coulomb of charge leaving the battery.

How much energy is transferred to an
external circuit
All the components connected across the terminals of a battery or power supply are collectively known as the external circuit.
external circuit
when 2 coulombs of charge flow out of a 9 V battery?
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How much charge must pass from a 6 V battery if 420 J of energy are transferred to an external circuit?
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Electrical energy is classified as one type of potential energy. Since the energy of the charges entering and leaving the buzzer is different, we can say that there is an 'electrical energy difference' across the buzzer. This is more commonly referred to as a potential difference or p.d. The size of the voltage across any component in a circuit is numerically the same as the potential difference. When describing electrical circuits the terms 'voltage' and 'p.d.' are often used interchangeably.

As well as having different voltages, batteries are available in a range of different physical sizes.

Figure 8.   Types of battery.
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Voltage V is measured in units of volts (V) if the energy W is measured in joules (J) and the charge Q is measured in coulombs (C). One volt is the electrical energy difference between two points if one
joule
The joule is the unit of energy.
joule
of electrical energy is transformed into other forms of energy when one coulomb of charge passes between the two points.

Calculate the voltage between two points when 25 C of charge release 10 J of energy when passing between the two points.
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An electron in a cathode ray tube is accelerated by moving through a p.d. of 5000 V. The charge on the electron is 1.6 × 10−19 C. The energy gained by the electron is …
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Voltage in series circuits
In Fig.9 the
LED
LED is the common abbreviation for a light emitting diode. When electrons and holes in an LED recombine, the excess energy produced is radiated as photons of light of one particular colour.
LED
and buzzer are connected in series with a power supply. Two of the voltmeters show the p.d.s across the components and the other shows the voltage supplied by the battery.

Click on the battery in Fig.9 and enter a value for the battery voltage in the range 0 to 20 V. Pay particular attention to the readings on the voltmeters.


Click on the figure below to interact with the model.

 Figure 9.  Voltages in a parallel circuit.



Complete the following statements for the circuit in Fig.9:

  • When the supply voltage is set to 15 V the p.d. across the LED is  V (to 1 d.p.). The p.d. across the buzzer is  V (to 1 d.p.). The voltage of the battery is  V (to the nearest whole number).
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When components are joined in series with a battery, the battery voltage is the sum of the voltages across the individual components. This can be expressed mathematically as:



If the supply voltage changes the voltages across each component changes but their sum always equals the supply voltage.

Voltage in parallel circuits
In Fig.10, the lamp and buzzer are connected in parallel and voltmeters are used to measure the p.d.s across various parts of the circuit. When the switch is closed, two of the voltmeters show the p.d.s across the components connected in parallel. The other voltmeter shows the total supplied by the battery.

Click on the battery and enter any value for the battery voltage in the range 0 to 20 V.


Click on the figure below to interact with the model.

 Figure 10.  Voltages in parallel circuits.



Set the battery voltage to 15 V and complete the sentences below by entering values for the voltages (to the nearest whole number).

  • The voltage across the buzzer is  V. The voltage across the lamp is  V. The battery voltage is  V.
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When components are joined in parallel the voltage across each of the branches in the parallel circuit is the same. This can be summarized mathematically as:



Altering the supply voltage alters the voltage but the voltage across each component is always the same.

EMF and potential difference
The idea of electric current that we have considered so far is based on energized charges flowing from a battery and delivering their energy to components such as buzzers and lamps. The charges then return to the battery to be re-energized.

The chemical reaction in the battery has the capacity to provide energy to the charges. The total energy provided by any power supply, such as a battery, to each coulomb of charge is called the EMF. The letters
EMF
EMF is the common abbreviation for the electromotive force – a measurement of a battery's capacity to provide energy to the charges.
EMF
stand for electromotive force. As a result you might think that this is a type of force, and that it should be measured in units of newtons. However, this is not the case!

The EMF is the energy supplied to each coulomb of charge leaving the battery and its units are therefore JC−1. These are exactly the same units as voltage, so EMF values can also be quoted in volts (V).


Click on the figure below to interact with the model.

 Figure 11.  Joining batteries.

Complete the following statements for the circuit in Fig.11.

  • When EMFs of 8 V and 4 V are connected together and joined in series with a buzzer and a lamp, the batteries provide voltages across the lamp and buzzer of  V and  V respectively.

    When EMFs of 6 V and 8 V are connected together and joined in series with a buzzer and a lamp, the batteries provide voltages across the lamp and buzzer of  V and  V respectively.

    EMFs of 3 V and  V are connected together and joined in series with a buzzer and a lamp. The batteries provide voltages across the lamp and buzzer of 2.06 V and 4.94 V respectively.
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In each of the cases in Fig.11 you should have noticed that the sum of the supply EMFs equals the sum of the p.d.s across the components.

The behaviour of the circuit in Fig.11 can be summarized mathematically in the equation:

EMFs of 30 V and 22 V are connected together in series with three other components. The p.d.s across two of the components are 17 V and 21 V. What is the p.d. across the third component?
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Electrical power
We can combine two of our existing equations to derive an expression for the electrical energy transformed per second (
electrical power
The electrical power dissipated by a component is the energy transferred per second when a current passes through the component.
electrical power
) in a circuit or component.

and

Combining these two equations gives

Rearranging this gives

The term W/t is the energy transferred per second. This is called the electrical power P which is measured in units of watts.
     Therefore



The energy transferred per second to an electrical component is called the electrical
power
The power of system is a measurement of the rate at which energy is transferred from one form to another. The scientific unit of power is the watt.
power
(P) and is measured in units of watts. Mathematically, electrical power is calculated from the equation:

Summary


Electrical current is the result of charges moving in a circuit. The magnitude of the current is defined as the rate of flow of charge and can be calculated using the equation below:



The current through all components connected in series is equal. In parallel circuits, the total current is the sum of the currents in the individual branches.

The EMF (electromotive force) of a battery is a measurement of its capacity to provide energy to the charges.

The magnitude of a voltage is defined as the energy supplied to each coulomb of charge. The voltage can be calculated using the equation:



The p.d.s across components connected in parallel are the same.

The total p.d. across components in series is equal to the sum of the p.d.s across the individual components.

The rate at which electrical energy is transferred to a component is called the electrical power. Power is calculated by multiplying the p.d. across by the current through the component:

Exercises
Figure 12.  
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1. In the circuit shown in Fig.12 a current of 2.5 A flows for 2 minutes. Calculate the total charge which passes through the resistor in this time.
  •  C   (to the nearest whole number)
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2. The p.d. across the resistor in Fig.12 is 6 V. How much energy is supplied to each coulomb of charge that passes through the resistor?
  •  J   (to the nearest whole number)
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3. Calculate the total quantity of energy passing through the resistor in Fig.12 during the two minutes.
  •  J   (to the nearest whole number)
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4. What happens to the temperature of the resistor in Fig.12?
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Figure 13.  
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5. In the circuit shown in Fig.13 the reading on ammeter A1 is 0.2 A. What is the reading on ammeter A2?
  •  A   (to 1 d.p.)
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6. In the circuit shown in Fig.14 two different resistors are connected to the 9 V battery. The reading on voltmeter V1 is 3.5 V. What is the reading on voltmeter V2?
  •  V   (to 1 d.p.)
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Figure 14.  
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7. When an ammeter is added to the circuit of Fig.14 it indicates a current of 0.2 A. What is the
resistance
The opposition to the flow of current provided by a circuit is called resistance. Resistance is measured in units called Ohms.
resistance
of R1?
  •  Ω   (to 1 d.p.)
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8. Calculate the resistance of R2?
  •  Ω   (to 1 d.p.)
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9. Calculate the total resistance of the circuit in Fig.14.
  •  Ω   (to the nearest whole number)
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10. A chemistry textbook states that in one mole of electrons there are 6 × 1023 electrons. The total charge of one mole of electrons is …
  •  C   (to the nearest whole number)
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11. In a certain electrochemical process a current of 5 A is supplied to a solution for 20 hours. Calculate the quantity of charge supplied to the solution.
  •  C   (to the nearest whole number)
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12. How many moles of electrons are supplied to the solution in the previous question?
  • moles   (to 2 d.p.)
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13. An electron with a charge of −1.6 × 10−19 C is placed at rest between charged plates as shown in Fig.15. The p.d. between the plates is set to 1500 V. The electron moves between the plates. Which of the explanations below is correct?
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Figure 15.  
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14. Calculate the
work
Work is the process by which energy is changed from one form to another. The scientific unit of work is the joule.
work
done by the electric field on the electron in Fig.15 as the electron moves between the plates.
  •  × 10−16 J   (to 1 d.p.)
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15. How much
kinetic energy
The kinetic energy of a system is a measurement of the energy associated with its translational motion.
kinetic energy
does the electron in Fig.15
gain
The gain of an amplifier is defined as the output voltage divided by the input voltage.
gain
in moving from the negative to the positive plate?
  •  × 10−16 J   (to 1 d.p.)
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16. The electron in Fig.15 is initially at rest. Calculate its speed just before it arrives at the positive plate. (The mass of the electron is 9.1 × 10−31kg.)
  •  × 107 ms−1   (to 1 d.p.)
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