Electromotive force and potential difference Revision Notes

Electromotive force, abbreviated as e.m.f., is defined as the total electrical work done by a source in moving a unit positive charge completely around a circuit. It represents the energy supplied by the source to each coulomb of charge as it passes through the source.

Physically, e.m.f. is the cause of current flow in a circuit. It is the energy per unit charge provided by the source to overcome the internal resistance of the source and any other components in the circuit.

The unit of e.m.f. is the volt (V), where 1 volt equals 1 joule per coulomb (1 V = 1 J/C).

• e.m.f. = work done by source / charge moved
• Unit: volt (V) = joule per coulomb (J/C)
• Represents energy supplied per unit charge

The relationship between work done (W), charge (Q), and electromotive force (E) is given by the formula:

\[ E = \frac{W}{Q} \] where: E is the e.m.f. in volts (V), W is the work done in joules (J), and Q is the charge in coulombs (C).

This formula can be rearranged to find work done or charge if the other quantities are known: \[ W = E \times Q \quad \text{or} \quad Q = \frac{W}{E} \]

• E = W/Q where E in volts, W in joules, Q in coulombs
• Rearrangements: W = E × Q, Q = W / E
• Example: If a source does 12 J of work to move 4 C, e.m.f. = 12 J / 4 C = 3 V

Electromotive force is the energy supplied per unit charge by the source when moving charge around the entire circuit, including overcoming internal resistance.

Potential difference (p.d.) is the energy used per unit charge when charge passes through a particular component or resistor in the circuit.

While both e.m.f. and p.d. are measured in volts and represent energy per unit charge, e.m.f. refers to the source's energy supply, and p.d. refers to energy used by components.

• e.m.f.: energy supplied per unit charge by source
• p.d.: energy used per unit charge by component
• Both measured in volts (V) but represent different energy transfers

In circuit diagrams, a source of e.m.f. such as a battery or cell is represented by a pair of lines: the longer line is the positive terminal and the shorter line the negative terminal.

The e.m.f. of a source is the maximum potential difference it can provide when no current flows (open circuit).

When current flows, some energy is lost overcoming the internal resistance of the source, so the terminal p.d. is less than the e.m.f.

• Battery symbol: long line (+), short line (-)
• e.m.f. is maximum voltage with no current (open circuit)
• Terminal p.d. < e.m.f. when current flows due to internal resistance

A battery does 24 joules of work to move 8 coulombs of charge around a circuit. Calculate the e.m.f. of the battery.

Using the formula: \[ E = \frac{W}{Q} = \frac{24\,\text{J}}{8\,\text{C}} = 3\,\text{V} \]

Therefore, the e.m.f. of the battery is 3 volts. This means the battery supplies 3 joules of energy to each coulomb of charge passing through it.

• Given: W = 24 J, Q = 8 C
• Calculate: E = W / Q = 24 J / 8 C = 3 V
• Answer: e.m.f. = 3 volts

Electromotive force, abbreviated as e.m.f., is defined as the energy supplied by an electrical source to move a unit positive charge around a complete circuit. It is the work done per unit charge by the source to maintain the flow of electric current.

Mathematically, e.m.f. (E) is given by the formula:

\[ E = \frac{W}{Q} \] where: W is the work done or energy supplied (in joules, J), and Q is the charge moved (in coulombs, C).

• e.m.f. is the energy supplied per coulomb of charge by a source.
• It is the cause of current flow in a circuit.
• It is measured in volts (V), where 1 V = 1 J/C.

The unit of electromotive force is the volt (V). One volt is defined as one joule of energy supplied per coulomb of charge moved.

In practical terms, e.m.f. is measured using a voltmeter connected across the terminals of a source when no current is drawn (open circuit). This ensures the reading reflects the maximum potential difference the source can provide, which equals its e.m.f.

Voltmeters used can be analogue or digital, and they must have a high resistance to avoid drawing current and altering the measurement.

• 1 volt = 1 joule per coulomb (1 V = 1 J/C).
• Measured using a voltmeter connected across the source terminals with no load.
• High resistance voltmeters prevent current flow during measurement.

Electromotive force represents the energy conversion performed by the source, such as a battery or generator, converting chemical or mechanical energy into electrical energy.

It provides the driving voltage that pushes charges through the circuit, overcoming resistance and enabling current flow.

The e.m.f. of a source is the maximum potential difference it can provide when no current flows. When current flows, the terminal potential difference is usually less due to internal resistance.

• e.m.f. is the maximum voltage a source can provide.
• It results from energy conversion inside the source.
• It drives current through the external circuit.

While both e.m.f. and potential difference are measured in volts, they differ in meaning and context.

Electromotive force refers to the energy supplied per unit charge by the source around the entire circuit.

Potential difference (p.d.) refers to the energy used per unit charge when passing through a component or part of the circuit, such as a resistor or lamp.

• e.m.f. is the energy supplied by the source per unit charge.
• Potential difference is the energy used by a component per unit charge.
• Both are measured in volts but represent different physical quantities.

A battery supplies 120 joules of energy to move 40 coulombs of charge around a circuit. Calculate the e.m.f. of the battery.

Using the formula: \[ E = \frac{W}{Q} \] Substitute the values: \[ E = \frac{120\ \text{J}}{40\ \text{C}} = 3\ \text{V} \]

Therefore, the e.m.f. of the battery is 3 volts. This means the battery supplies 3 joules of energy for every coulomb of charge moved around the circuit.

• Formula: \( E = \frac{W}{Q} \)
• Substitute: \( W = 120\ \text{J}, Q = 40\ \text{C} \)
• Calculate: \( E = 3\ \text{V} \)

Potential difference (p.d.) between two points in an electrical circuit is defined as the work done to move a unit positive charge from one point to the other through a component.

Mathematically, potential difference V is given by the equation:

\[ V = \frac{W}{Q} \] where: W is the work done (in joules, J) on the charge Q (in coulombs, C).

• Potential difference is the energy transferred per unit charge.
• It is a scalar quantity, having magnitude only.
• The unit of potential difference is the volt (V), where 1 V = 1 J/C.

When a charge moves through a component such as a resistor, battery, or lamp, energy is transferred to or from the charge.

The potential difference across the component indicates how much energy each coulomb of charge gains or loses.

For example, in a resistor, electrical energy is converted into heat, so the potential difference corresponds to the energy converted per coulomb of charge passing through it.

• Higher potential difference means more energy transferred per unit charge.
• Potential difference drives current flow in a circuit by providing energy to charges.

The formula for potential difference is: \[ V = \frac{W}{Q} \] where:

\(V\) is potential difference in volts (V), \(W\) is work done in joules (J), \(Q\) is charge in coulombs (C).

To calculate potential difference, rearrange the formula as needed and substitute known values.

• Example calculation:
• If 12 J of work is done to move 3 C of charge through a component, then:
• \[ V = \frac{12\,\text{J}}{3\,\text{C}} = 4\,\text{V} \]
• Common error: confusing charge (C) with current (A).

Potential difference is measured using a voltmeter connected in parallel across the component.

Voltmeters have high resistance to avoid drawing current and affecting the circuit.

Both analogue and digital voltmeters can be used, with appropriate voltage ranges selected for accuracy.

• Always connect the voltmeter in parallel with the component.
• Select the correct voltage range to prevent damage and ensure accurate readings.

To draw a circuit diagram showing potential difference:

1. Draw a simple circuit with a battery, resistor, and connecting wires.

2. Label the battery terminals with '+' and '-' signs indicating polarity, showing the direction of potential difference across the resistor from higher to lower potential (from positive to negative terminal).

• Indicate the voltmeter connected in parallel across the resistor.
• Use arrows to show the direction of positive charge flow (conventional current).

Potential difference between two points in an electrical circuit is defined as the work done or energy transferred to move a unit positive charge from one point to another.

Mathematically, potential difference (V) is given by the formula:

\[ V = \frac{W}{Q} \] where: W = work done or energy transferred (in joules, J), Q = charge moved (in coulombs, C).

• Potential difference is a scalar quantity.
• It represents energy per unit charge.
• It is the cause of current flow in a circuit.

The unit of potential difference is the volt (V). One volt is defined as one joule of energy transferred per coulomb of charge moved:

\[ 1\ \text{volt} = 1\ \text{joule per coulomb} = 1\ \text{J/C} \]

This means if 1 coulomb of charge gains or loses 1 joule of energy moving between two points, the potential difference between those points is 1 volt.

• Volt is a derived SI unit.
• Volt is abbreviated as V.
• Potential difference is often called voltage.

When a charge moves through a component in a circuit, energy is transferred either from electrical energy to other forms (e.g., light, heat) or vice versa.

The potential difference between two points indicates how much energy each coulomb of charge gains or loses moving between those points.

For example, a 12 V battery transfers 12 joules of energy to each coulomb of charge passing through it.

• Potential difference drives current through components.
• Higher potential difference means more energy transferred per charge.
• It is essential for powering electrical devices.

A voltmeter measures the potential difference between two points in a circuit.

It must be connected in parallel across the component or section of the circuit where the potential difference is to be measured.

Voltmeters have a very high resistance to ensure they draw negligible current and do not affect the circuit operation.

• Connect voltmeter in parallel.
• Use appropriate voltage range on the voltmeter.
• Digital voltmeters display readings directly in volts.
• Analogue voltmeters use a pointer and scale.

Calculate the potential difference across a resistor if 5 coulombs of charge transfer 20 joules of energy through it.

Using the formula: \[ V = \frac{W}{Q} = \frac{20\ \text{J}}{5\ \text{C}} = 4\ \text{V} \]

Therefore, the potential difference across the resistor is 4 volts.

• Show formula substitution.
• Include units in calculation.
• Answer must include unit V.
• Common error: forgetting to include units or mixing up energy and charge.

A voltmeter is an instrument designed to measure the potential difference, or voltage, between two points in an electrical circuit. Voltage is the work done per unit charge to move charges between those points and is measured in volts (V).

Voltmeters must have a very high resistance to ensure they draw minimal current from the circuit, preventing significant alteration of the circuit conditions during measurement.

Voltmeters are connected in parallel across the component or section of the circuit where the voltage is to be measured.

• Measures potential difference (voltage) in volts (V).
• Connected in parallel to the component.
• High internal resistance to minimise current draw.

Analogue voltmeters use a moving coil galvanometer mechanism. The voltage causes a current to flow through the coil, producing a magnetic force that moves a needle across a calibrated scale.

The scale is usually non-linear, especially at lower ranges, so careful reading is required.

Analogue voltmeters have multiple selectable ranges, each with a different maximum voltage. The user selects the range expected to be just above the voltage to be measured to maximise accuracy and protect the instrument.

• Uses a needle and dial scale.
• Non-linear scale requires careful reading.
• Multiple ranges selectable by the user.
• Higher range reduces sensitivity but prevents damage.

Digital voltmeters convert the analogue voltage signal into a digital number displayed on an LCD or LED screen.

They typically have a linear scale and provide direct numerical readings, reducing reading errors compared to analogue meters.

Digital voltmeters also have selectable ranges, but many modern DVMs include an auto-ranging feature that automatically selects the appropriate range for the voltage measured, simplifying use and improving accuracy.

• Displays numerical voltage reading digitally.
• Linear scale, easier to read accurately.
• Selectable ranges or auto-ranging feature.
• Less prone to parallax errors than analogue meters.

Selecting the correct measurement range directly affects the result for accurate readings and to protect the voltmeter from damage.

If the range is set too low, the meter may be overloaded, potentially damaging the instrument or causing the needle to peg at maximum.

If the range is set too high, the reading will be less precise because the scale is less sensitive over a large range, making small voltage differences harder to detect.

• Choose a range slightly higher than expected voltage.
• Avoid overloading the meter to prevent damage.
• Lower ranges provide more precise readings.
• Auto-ranging digital meters simplify this process.

To measure voltage, connect the voltmeter leads across the component or section of the circuit where the voltage is to be measured, ensuring correct polarity: the positive lead to the higher potential point and the negative lead to the lower potential point.

Always start with the highest voltage range if the expected voltage is unknown, then switch to lower ranges for more precise readings if safe to do so.

Ensure the voltmeter is connected in parallel, never in series, as series connection would affect the circuit operation and give incorrect readings.

• Connect voltmeter in parallel across the component.
• Observe correct polarity for accurate readings.
• Start with highest range if voltage unknown.
• Never connect voltmeter in series.

Electromotive force, abbreviated as e.m.f. and symbolised by E, is the energy supplied by a source per unit charge that passes through it. It represents the work done by the source to move charge completely around a circuit, overcoming internal resistance and other energy losses.

Mathematically, e.m.f. is defined as the ratio of the work done (W) by the source in joules (J) to the charge (Q) moved in coulombs (C):

E = W / Q. This formula shows that e.m.f. is the energy provided per coulomb of charge.

• E = electromotive force (volts, V)
• W = work done by the source (joules, J)
• Q = charge moved (coulombs, C)

The e.m.f. of a source indicates how much energy it can supply to each coulomb of charge passing through it. For example, a 12 V battery supplies 12 joules of energy for every coulomb of charge it moves around the circuit.

Since work is measured in joules and charge in coulombs, the unit of e.m.f. is volts (V), where 1 V = 1 J/C.

It is important to note that e.m.f. is not a force but a potential difference generated by the source.

• Unit of e.m.f.: volt (V)
• 1 V = 1 joule per coulomb (1 V = 1 J/C)

Electromotive force refers to the energy supplied per unit charge by the source to move charge around the entire circuit, including overcoming internal resistance.

Potential difference (p.d.) is the energy used per unit charge as it passes through a component in the circuit, such as a resistor or lamp.

While both e.m.f. and p.d. are measured in volts and involve energy per unit charge, e.m.f. is the total energy supplied, and p.d. is the energy converted or used in a part of the circuit.

• E.m.f. is the energy supplied per coulomb by the source
• Potential difference is the energy used per coulomb by a component

To calculate the electromotive force, rearrange the formula as needed depending on the known quantities.

Example: A battery does 60 J of work to move 20 C of charge around a circuit. Calculate the e.m.f.

Step 1: Write the formula: E = W / Q Step 2: Substitute values: E = 60 J / 20 C Step 3: Calculate: E = 3 V Answer: The e.m.f. of the battery is 3 volts (3 V).

• Show substitution of values with correct units
• Calculate and include units in the final answer

To draw a simple circuit illustrating e.m.f.: 1. Draw a closed loop with a battery symbol (two parallel lines, the longer line representing the positive terminal). 2. Label the battery with its e.m.f. value, e.g., 12 V. 3. Include a resistor or lamp in the circuit to show where potential difference occurs. 4. Indicate the direction of current flow from the positive to the negative terminal. 5. Label the work done by the battery as W and the charge moved as Q to connect with the formula E = W/Q.

• Battery symbol with e.m.f. labelled
• Current direction arrow
• Component with potential difference indicated

Potential difference between two points in an electric circuit is the amount of work done to move a unit positive charge from one point to the other. It represents the energy transferred per coulomb of charge passing through a component or between two points.

Potential difference is a scalar quantity measured in volts (V). One volt is defined as one joule of work done per coulomb of charge moved: 1 V = 1 J/C.

• Potential difference (V) = Work done (W) / Charge (Q)
• Units: V in volts (V), W in joules (J), Q in coulombs (C)

The formula for potential difference is: V = W / Q, where:

V is the potential difference in volts (V) W is the work done in joules (J) Q is the charge moved in coulombs (C)

This formula can be rearranged to find work done or charge if the other quantities are known: W = V × Q Q = W / V

• Use consistent SI units when calculating potential difference.
• Always include units in calculations to ensure correctness.

Calculate the potential difference across a resistor if 120 J of work is done to move 4 C of charge through it.

Step 1: Write down the formula: V = W / Q Step 2: Substitute values: V = 120 J / 4 C Step 3: Calculate: V = 30 V Step 4: State the answer with units: The potential difference is 30 volts.

• Common error: forgetting to include units or mixing units (e.g., using mC instead of C without conversion).
• Always check that charge is in coulombs and work is in joules before calculating.

Potential difference indicates how much energy each coulomb of charge gains or loses when moving between two points. For example, in a battery, the potential difference between terminals shows how much energy the battery can supply per coulomb of charge.

In a circuit component like a resistor, the potential difference corresponds to energy converted to other forms (e.g., heat) per coulomb of charge passing through it.

• Potential difference drives current through components.
• It is measured using a voltmeter connected in parallel across the component.

To draw a circuit diagram showing potential difference measurement:

1. Draw a simple circuit with a battery, a resistor, and connecting wires.

2. Place a voltmeter symbol (circle with a 'V' inside) connected in parallel across the resistor terminals, indicating it measures the potential difference across the resistor.

• Voltmeter must be connected in parallel to measure potential difference correctly.
• The voltmeter ideally has very high resistance to avoid drawing current.