Introduction


Recent decades have seen a huge expansion in consumer electronics. While the functions of new devices differ widely, their power still largely comes from either batteries or mains power supplies.



In the simple circuits met so far, we have pictured power supplies as being able to provide as much current as the components require. In reality, this is not the case.

The

energy

A system has energy when it has the capacity to do work. The scientific unit of energy is the joule.energy provided by any

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 supply, such as a battery, to each

coulomb

The coulomb is the unit of charge. One coulomb is approximately equivalent to the charge carried by 6.25 × 10¹⁸ electrons.coulomb of charge leaving a battery or

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 supply is called the

electromotive force

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

EMF

EMF is the common abbreviation for the electromotive force – a measurement of a battery's capacity to provide energy to the charges.EMF. The electromotive force is measured in units of joules per

coulomb

The coulomb is the unit of charge. One coulomb is approximately equivalent to the charge carried by 6.25 × 10¹⁸ electrons.coulomb (JC⁻¹) or volts (V).


Click on the figure below to interact with the model.




Turn on the circuit in Fig.1 by clicking on the switch. Then connect the voltmeters across the buzzer and lamp by dragging them into the spaces in the circuit. Note the values for the p.d.s across the two components.



You should have discovered one example of a general rule which states that the sum of the battery EMFs is always equal to the sum of the p.d.s across the components. This can be summarized in the equation below:



Confirm that the sum of the battery EMFs is always equal to the sum of the p.d.s across the components by changing the values of the battery voltages in Fig.1. To do this, click on the battery voltages and alter their values in the range 0–10 V.

In Fig.1, the buzzer and the lamp were attached to the terminals of the batteries. They could just as easily have been connected to the output terminals of a power supply. When any set of components is connected across the terminals of a battery or a power supply like this, they are collectively called the external circuit. This is to distinguish such components from the internal circuit within the power supply. 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 the

external circuit

All the components connected across the terminals of a battery or power supply are collectively known as the external circuit.external circuit is often referred to as the load resistance.



In Fig.1 the load resistance is the only resistance in the circuit. However, this is not the case in the circuit in Fig.2 below.


Click on the figure below to interact with the model.




Again, move the voltmeters into place to measure the p.d. across the two components.



We can explain the 'lost volts' in Fig.2 by the fact that the LED and the lamp are not the only sources of resistance in the circuit. In fact, the battery also has a small internal resistance.

Any battery or power supply with an

internal resistance

All batteries or power supplies have internal resistance. This resistance has the effect of reducing the output p.d. as the current supplied increases.internal resistance can be pictured as shown in Fig.3. Here, the internal resistance of 2 Ω is shown as a resistor in series with the power source.



Internal resistance is a feature of all practical power supplies. Different designs of battery will have different internal resistances, and the manufacturers will often take steps to minimize the internal resistance.


The 12 V output from a car battery will have the same output

voltage

The voltage across a component is the electrical energy transferred by 1 coulomb of charge passing through the component.voltage as a 12 V domestic battery. However, the car battery needs to have a much lower internal resistance and the design needed to achieve this results in the car battery being larger and heavier.

The voltmeter in the Fig.4 below shows the 'lost volts', even though in practice this is a quantity that could not be measured experimentally.


Click on the figure below to interact with the model.




Set the variable resistor in the circuit of Fig.4 to 10 Ω. Close the switch and note the values of the p.d.s across the internal resistance and the load resistor.



The p.d. actually available at the battery terminals is called the terminal p.d. If the EMF of the battery is E, the

terminal p.d.

The terminal p.d. is the voltage available at the terminals of a battery or power supply. The terminal p.d. varies depending on how much current is being drawn.terminal p.d. is V_tpd and the p.d. across the internal resistance is V_lost, we can say:



The above equation holds, no matter what the value of the load resistor or the

current

The rate of flow of charge past any specific point in a circuit. The base unit of current is the Ampere.current drawn from the supply. We can verify this using Fig.4. Set the variable resistor to a value of 60 Ω.



Check this again for another value of the variable resistor.

Fig.5 below shows two identical circuits allowing different numbers of lamps to be connected to the batteries. Circuit B has internal resistance in the battery, whereas Circuit A shows the hypothetical case where there is no internal resistance.


Click on the figure below to interact with the model.




Complete the following table for Circuit A.





Now complete the following table for Circuit B.





Fig.5 demonstrates clearly that, when a battery has internal resistance, increasing the current taken from the battery reduces the voltage available to the external circuit. This is why manufacturers of power supplies and batteries often try to reduce the internal resistance of their products.

When a power supply or battery has internal resistance, increasing the current provided to an external circuit reduces the p.d. across this circuit. As the current taken from the supply increases, the current through the internal resistance increases and so more of the p.d. will be across the internal resistance. Consequently less p.d. will be available for the external circuit. We can see this idea mathematically by using the equation from above:



where E is the EMF, V_tpd is the p.d. across the terminals of the battery, and V_lost is the 'lost' voltage.




If the current becomes sufficiently large, the output p.d. will fall to zero. The value of current for which this happens is called I_max.


Click on the figure below to interact with the model.




The battery in Fig.6 above has an internal resistance (which is not shown on the circuit diagram). Use the variable resistor to alter the current drawn from the battery and observe how the current varies.



When the resistance across the battery is zero, we say that the battery is short-circuited. Maximum current flows when the battery is short-circuited.

We have seen what happens when the maximum current is obtained from a power supply. Alternatively, if no current is drawn from the supply, the output voltage V_tpd and the EMF E of the battery are equal.

We can again show this idea mathematically by reusing the equation from above:


 



The EMF of the supply is equal to the output p.d. when no current is being supplied.


Click on the figure below to interact with the model.




The battery in Fig.7 above has an internal resistance (which is not shown on the circuit diagram). Use the variable resistor to alter the current drawn from the battery and observe how the p.d. across the bulb varies.




Click on the figure below to interact with the model.




Close the switch to see how the reading on the voltmeter in Fig.8 changes.

In Fig.9 a variable resistor is connected to a battery. We will use this circuit to determine the EMF, the maximum current, and the internal resistance of the battery.


Click on the figure below to interact with the model.




Adjust the variable resistor to alter the current passing through the circuit in Fig.9 above.



Set the variable resistor in Fig.9 to a range of different positions and enter values for the terminal p.d. V_tpd, and the current I into the table of Fig.10.



The line in the graph of Fig.10 is given by the equation E = V_tpd + Ir. We can use this equation to explain the shape of the line.




On the graph, the value of I_max is given by the point at which the line cuts the x-axis. By extending the line in Fig.10 to where it cuts the x-axis, we can find the value for I_max.



We have already seen that the EMF is the largest voltage available from the battery, and that this occurs when I = 0. On the graph, this is illustrated by the point where the line cuts the graph's y-axis.



Now that we know the values of the EMF and the short-circuit current I_max we can calculate the internal resistance of the battery. The steps below lead through the analysis of how to do this.




Alternatively we can use the data in a different way to find the internal resistance of the power source. The line in the graph of Fig.10 is given by the equation:



Click on the V_tpd term to rearrange the equation. It is now in the standard form 'y = mx + c' where V_tpd is the variable plotted on the y-axis and I the variable plotted on the x-axis. The intercept gives the EMF of the supply and the negative of the gradient indicates its internal resistance.



The graph above shows the graph of terminal p.d. plotted against current for a power supply.

The experimental data generated from Fig.10 shows the different currents passing through a resistor for different values of the p.d. across it. We can multiply these values to get the power dissipated in the resistor at different currents. Similarly we can use

Ohm's Law

Ohm's Law states that at constant temperature the current in a conductor is directly proportional to the d.p. across the conductor. The constant of proportionality is called the resistance of the sample.Ohm's Law to get the values of the resistance connected to the battery by simply dividing the p.d. readings by the current readings.



A graph of power delivered versus load resistance shows that the power delivered to the external circuit is not constant. The power delivered rises to a maximum when the internal and external resistances are equal.

Summary


All the components connected across the terminals of a battery or power supply are collectively known as the external circuit. The total resistance of these components is known as the load resistance.

All batteries or power supplies have internal resistance. This resistance has the effect of reducing the output p.d. as the current supplied increases.

The output p.d. V_tpd for any current I can be found using the equation:



where E is the EMF of the supply and r is the internal resistance of the supply.

If the EMF of the power supply and the short-circuit current I_max are known, the internal resistance of the supply can be determined using the equation below: