The same current at every point

Definition

Single closed loop

A circuit with only one conducting path, so all of the charge passes through every component in turn.

Definition

Conservation of charge

The principle that charge cannot be created or destroyed, only moved from one place to another.

A single closed loop is a circuit with only one path for the charge, so charge leaving the source passes through every component in turn before returning.
A torch, with its cells, switch and lamp joined in one ring, is a single closed loop.
In a single closed loop, the current has the same value at every point.
The current just after the cell, the current between two components and the current just before the charge returns to the cell are all equal.
The current is not used up by lamps, motors, resistors or any other component.
The amount of charge that enters a component each second is exactly equal to the amount of charge that leaves it each second.
This follows from the conservation of charge, because charge cannot be destroyed inside a component and, in a steady circuit, it does not pile up there either.
A component transfers energy from the circuit, but the charge flowing through it is not lost, so the current after a component equals the current before it.
Every part of the loop is already full of free electrons, so when the switch closes, electrons all the way round the loop start drifting at the same moment.
A bicycle chain behaves in a similar way, because every link moves round at the same rate and no link is used up as it passes the gears.
If the loop is changed, for example by adding another lamp, the size of the current may change, but it changes everywhere in the loop at once and is still the same at every point.
This rule applies only when there is a single path for the charge.

Measuring current in a loop

Definition

Ammeter

A meter connected in series with a component to measure the current through it.

Current is measured with an ammeter, which is connected in series.
Connecting in series means the loop is opened at one point and the ammeter is placed in the gap, so that all of the charge flows through the meter.
In a single closed loop, an ammeter gives the same reading wherever it is placed, whether that is next to the cell, before a lamp, after a lamp or between two components.
Several ammeters placed in the same loop all show the same reading, apart from tiny differences caused by the resolution of the meters.
Two different components in the same loop can behave very differently, such as one lamp glowing brightly and another glowing dimly, yet the ammeter shows the same current through each.
Brightness is therefore not a reliable way to judge where the current is largest in a single loop.

Practical

Measuring current around a single loop

Aim: to show that the current is the same at every point in a single closed loop.
Apparatus: a low-voltage power supply or battery pack of about $V3\ \text{V}$ , two different lamps in holders, a switch, one digital ammeter (or three identical ammeters), and connecting leads.
Method, setting up:
- Draw a circuit diagram of a single loop containing the supply, the switch and the two lamps, and mark four positions for the ammeter: after the supply, between the switch and the first lamp, between the two lamps, and after the second lamp.
- Check that the ammeter reads zero before connecting it, and note any zero error so that it can be subtracted from each reading.
- Build the loop from the diagram with the switch open, placing the ammeter at the first position so that the charge must pass through it.
Method, taking readings:
- Close the switch, wait for the reading to settle, record the current to the resolution of the meter, then open the switch.
- Move the ammeter to the next position by opening the loop at that point and reconnecting it with the ammeter in the gap.
- Repeat until a reading has been taken at all four positions.
- Repeat the whole set of readings two more times and calculate the mean current at each position.
- Note the brightness of each lamp while the switch is closed.
Results: the mean current is the same at all four positions, for example $A0.24\ \text{A}$ , even if the two lamps glow with different brightness.
Conclusion: the current is the same at every point in a single closed loop, so the lamps do not use up current.
Watch out: connecting the ammeter across a lamp instead of in the loop gives a wrong reading and can damage the meter, and a meter that does not read zero beforehand adds the same error to every reading.
Safety: use a low-voltage supply, open the switch before moving the ammeter, and do not touch the lamps after use, because they become hot.

Example

Reading ammeters in a single loop

A loop contains a cell, a lamp, a motor and a resistor, with ammeters $A1\text{A}_1$ , $A2\text{A}_2$ and $A3\text{A}_3$ placed between the components.
Ammeter $A1\text{A}_1$ reads $A0.36\ \text{A}$ .
The circuit has no branches, so all of the charge passes through every component and every ammeter.
The current is the same at every point, so $A2\text{A}_2$ and $A3\text{A}_3$ both read $A0.36\ \text{A}$ .
A second lamp is then added to the same loop, and $A1\text{A}_1$ now reads $A0.24\ \text{A}$ .
The current has changed, but it has changed everywhere at once, so $A2\text{A}_2$ and $A3\text{A}_3$ now both read $A0.24\ \text{A}$ .

Common Mistake

Do not say that current is used up by a component, because the same amount of charge leaves a component each second as enters it.
Do not say that current is shared between the components in a single loop, because every component carries the full current.
Do not assume the brighter lamp carries the larger current when both lamps are in the same loop.

Exam technique

Answering single-loop ammeter questions

Check that the circuit has no branches before applying the rule.
Give the reading as a number with its unit, such as $A0.36\ \text{A}$ , copying the value from the ammeter you are given.
When asked to explain, add the reason that the current is the same at all points in a single closed loop.
If asked why this is true, link it to charge: charge is not used up, so the rate of flow of charge is the same everywhere.

Self review

State how the current at one point in a single closed loop compares with the current at any other point.
Explain why a lamp does not use up current.
Describe how an ammeter must be connected to measure the current in a loop.
An ammeter before a lamp reads $A0.50\ \text{A}$ . State the reading on an ammeter after the lamp in the same single loop.
Explain why a dim lamp and a bright lamp in the same single loop carry the same current.

The same current at every point

Definition

Single closed loop

A circuit with only one conducting path, so all of the charge passes through every component in turn.

Definition

Conservation of charge

The principle that charge cannot be created or destroyed, only moved from one place to another.

A single closed loop is a circuit with only one path for the charge, so charge leaving the source passes through every component in turn before returning.
A torch, with its cells, switch and lamp joined in one ring, is a single closed loop.
In a single closed loop, the current has the same value at every point.
The current just after the cell, the current between two components and the current just before the charge returns to the cell are all equal.
The current is not used up by lamps, motors, resistors or any other component.
The amount of charge that enters a component each second is exactly equal to the amount of charge that leaves it each second.
This follows from the conservation of charge, because charge cannot be destroyed inside a component and, in a steady circuit, it does not pile up there either.
A component transfers energy from the circuit, but the charge flowing through it is not lost, so the current after a component equals the current before it.
Every part of the loop is already full of free electrons, so when the switch closes, electrons all the way round the loop start drifting at the same moment.
A bicycle chain behaves in a similar way, because every link moves round at the same rate and no link is used up as it passes the gears.
If the loop is changed, for example by adding another lamp, the size of the current may change, but it changes everywhere in the loop at once and is still the same at every point.
This rule applies only when there is a single path for the charge.

Measuring current in a loop

Definition

Ammeter

A meter connected in series with a component to measure the current through it.

Current is measured with an ammeter, which is connected in series.
Connecting in series means the loop is opened at one point and the ammeter is placed in the gap, so that all of the charge flows through the meter.
In a single closed loop, an ammeter gives the same reading wherever it is placed, whether that is next to the cell, before a lamp, after a lamp or between two components.
Several ammeters placed in the same loop all show the same reading, apart from tiny differences caused by the resolution of the meters.
Two different components in the same loop can behave very differently, such as one lamp glowing brightly and another glowing dimly, yet the ammeter shows the same current through each.
Brightness is therefore not a reliable way to judge where the current is largest in a single loop.

Practical

Measuring current around a single loop

Aim: to show that the current is the same at every point in a single closed loop.
Apparatus: a low-voltage power supply or battery pack of about $V3\ \text{V}$ , two different lamps in holders, a switch, one digital ammeter (or three identical ammeters), and connecting leads.
Method, setting up:
- Draw a circuit diagram of a single loop containing the supply, the switch and the two lamps, and mark four positions for the ammeter: after the supply, between the switch and the first lamp, between the two lamps, and after the second lamp.
- Check that the ammeter reads zero before connecting it, and note any zero error so that it can be subtracted from each reading.
- Build the loop from the diagram with the switch open, placing the ammeter at the first position so that the charge must pass through it.
Method, taking readings:
- Close the switch, wait for the reading to settle, record the current to the resolution of the meter, then open the switch.
- Move the ammeter to the next position by opening the loop at that point and reconnecting it with the ammeter in the gap.
- Repeat until a reading has been taken at all four positions.
- Repeat the whole set of readings two more times and calculate the mean current at each position.
- Note the brightness of each lamp while the switch is closed.
Results: the mean current is the same at all four positions, for example $A0.24\ \text{A}$ , even if the two lamps glow with different brightness.
Conclusion: the current is the same at every point in a single closed loop, so the lamps do not use up current.
Watch out: connecting the ammeter across a lamp instead of in the loop gives a wrong reading and can damage the meter, and a meter that does not read zero beforehand adds the same error to every reading.
Safety: use a low-voltage supply, open the switch before moving the ammeter, and do not touch the lamps after use, because they become hot.

Example

Reading ammeters in a single loop

A loop contains a cell, a lamp, a motor and a resistor, with ammeters $A1\text{A}_1$ , $A2\text{A}_2$ and $A3\text{A}_3$ placed between the components.
Ammeter $A1\text{A}_1$ reads $A0.36\ \text{A}$ .
The circuit has no branches, so all of the charge passes through every component and every ammeter.
The current is the same at every point, so $A2\text{A}_2$ and $A3\text{A}_3$ both read $A0.36\ \text{A}$ .
A second lamp is then added to the same loop, and $A1\text{A}_1$ now reads $A0.24\ \text{A}$ .
The current has changed, but it has changed everywhere at once, so $A2\text{A}_2$ and $A3\text{A}_3$ now both read $A0.24\ \text{A}$ .

Common Mistake

Do not say that current is used up by a component, because the same amount of charge leaves a component each second as enters it.
Do not say that current is shared between the components in a single loop, because every component carries the full current.
Do not assume the brighter lamp carries the larger current when both lamps are in the same loop.

Exam technique

Answering single-loop ammeter questions

Check that the circuit has no branches before applying the rule.
Give the reading as a number with its unit, such as $A0.36\ \text{A}$ , copying the value from the ammeter you are given.
When asked to explain, add the reason that the current is the same at all points in a single closed loop.
If asked why this is true, link it to charge: charge is not used up, so the rate of flow of charge is the same everywhere.

Self review

State how the current at one point in a single closed loop compares with the current at any other point.
Explain why a lamp does not use up current.
Describe how an ammeter must be connected to measure the current in a loop.
An ammeter before a lamp reads $A0.50\ \text{A}$ . State the reading on an ammeter after the lamp in the same single loop.
Explain why a dim lamp and a bright lamp in the same single loop carry the same current.

3.1.6 Current in a single closed loop

The same current at every point

Measuring current in a loop

Measuring current around a single loop

Reading ammeters in a single loop

Answering single-loop ammeter questions

Review 3.1.6 Current in a single closed loop by teaching Genie

3.1.6 Current in a single closed loop

The same current at every point

Measuring current in a loop

Measuring current around a single loop

Reading ammeters in a single loop

Answering single-loop ammeter questions

Review 3.1.6 Current in a single closed loop by teaching Genie

3.1.6 Current in a single closed loop

The same current at every point

Measuring current in a loop

Measuring current around a single loop

Reading ammeters in a single loop

Answering single-loop ammeter questions

Review 3.1.6 Current in a single closed loop by teaching Genie

3.1.6 Current in a single closed loop Revision Guide

3.1.6 Current in a single closed loop

The same current at every point

Measuring current in a loop

Measuring current around a single loop

Reading ammeters in a single loop

Answering single-loop ammeter questions

Review 3.1.6 Current in a single closed loop by teaching Genie

3.1.6 Current in a single closed loop Revision Guide