Why do real cells warm up when delivering current?

Internal resistance dissipates energy as heat when current flows. This internal heating reduces terminal p.d. and reveals the non-ideal nature of real power sources.

Why does terminal p.d. decrease as current increases?

A larger current causes a greater voltage drop across internal resistance, increasing internal energy loss. As a result, less energy per coulomb remains available to the external circuit.

Why does an ideal power supply have terminal p.d. equal to e.m.f.?

An ideal supply has zero internal resistance, so no energy is lost inside the source. All supplied energy per charge is available to the external circuit, making terminal p.d. equal to e.m.f.

What is the key difference between e.m.f. and terminal p.d.?

E.m.f. is the maximum energy supplied per coulomb with no current flowing, while terminal p.d. is the energy per coulomb available to the external circuit when current flows. Terminal p.d. is lower because some energy is lost inside the source due to internal resistance.

Why is terminal p.d. always less than e.m.f. when current flows?

Internal resistance causes some electrical energy to be converted into heat inside the source. Because this energy is lost internally, the external circuit receives less energy per coulomb than the source's maximum e.m.f.

How do lost volts differ from terminal p.d.?

Lost volts represent the energy per coulomb dissipated inside the cell due to internal resistance, whereas terminal p.d. is the usable energy delivered to the load. Their sum equals the total energy supplied per coulomb, which is the e.m.f.

What mistake occurs if terminal p.d. is assumed equal to e.m.f. during current flow?

This assumption ignores internal resistance and overestimates the voltage available to the circuit. It leads to incorrect current and power predictions because real sources always lose some energy internally.

Why is it incorrect to apply $V = I(R+r)$ when calculating terminal p.d.?

This formula gives the full e.m.f., not the terminal p.d., because it includes both internal and external voltage drops. Using it would incorrectly treat internal losses as available voltage.

What error occurs if internal resistance is omitted from a circuit that includes it?

Omitting internal resistance leads to underestimating voltage losses and overestimating terminal p.d. and current. This mistake can significantly distort the predicted behavior of practical circuits.

What is e.m.f. in a circuit?

E.m.f. is the energy supplied per unit charge by a power source. It represents the maximum potential difference the source can provide when no current flows.

E.M.F. vs. Terminal Potential Difference | Pearson Edexcel International A-Level Physics

1. Definition & Core Concepts

Electromotive Force (e.m.f.) is the energy transferred from a power supply to each coulomb of charge, describing how much energy the source makes available before any internal losses occur. It represents the maximum possible potential difference when no current flows.
Terminal Potential Difference is the actual potential difference measured across the terminals of a power source when a current is flowing. It is always equal to or less than the e.m.f. because internal resistance causes some energy loss inside the source.
Internal Resistance refers to the inherent resistance within a power source that converts some electrical energy into heat. This resistance reduces the voltage available to external components under load.
Lost Volts represent the energy per unit charge dissipated inside the power source due to internal resistance. They quantify how much potential is unavailable to the external circuit.

Diagram showing a cell with internal resistance r and external resistor R

2. Underlying Principles

Energy conservation in electrical sources explains why e.m.f. equals the sum of terminal p.d. and lost volts. Energy supplied per unit charge must equal the energy delivered to external components plus energy dissipated internally.
Ohm’s law applied separately to the internal and external resistances provides the relationships $V = IR$ for the terminal p.d. and $V_r = Ir$ for lost volts. These show how current simultaneously determines useful and wasted voltage.
Series resistance behavior indicates that internal and external resistances add directly, meaning the total supply voltage distributes between them based on their relative magnitudes.
Load dependence of terminal p.d. arises because higher current increases the voltage drop across internal resistance. Thus, heavier loads cause a lower terminal p.d., illustrating the dynamic behavior of real power sources.

3. Methods & Techniques

Calculating terminal p.d. involves applying $V = IR$ , where $I$ is the current in the circuit and $R$ is the external load. This provides the voltage available to external components under operating conditions.
Finding lost volts uses the relation $V_r = Ir$ , capturing how internal resistance reduces usable voltage. This method is crucial when evaluating efficiency and heating inside the cell.
Relating e.m.f., terminal p.d., and lost volts uses the identity $\varepsilon = V + Ir$ . This formula allows solving for any of the three quantities depending on the known variables.
Selecting measurement conditions requires recognizing that e.m.f. is measured under open-circuit conditions, while terminal p.d. is measured during current flow. This prevents mixing incompatible readings.

4. Key Distinctions

Comparison Table

Feature	E.M.F.	Terminal Potential Difference
Definition	Energy supplied per coulomb	Energy available per coulomb to external circuit
Measured When	No current flows	Current flows through external load
Affected by Internal Resistance	No	Yes, always lower than e.m.f.
Mathematical Form	$\varepsilon$	$V = IR$
Conceptual Meaning	Input energy	Output usable energy

5. Exam Strategy & Tips

Identify whether current flows by checking if the circuit is open or closed. This determines whether you should use e.m.f. or terminal p.d., avoiding misapplication of formulas.
Check for internal resistance explicitly in diagrams, since neglecting internal resistance gives incorrect current and voltage predictions when it is present.
Use consistent variables by carefully distinguishing between total voltage (e.m.f.), terminal p.d., and lost volts. Examiners often test confusion among these related quantities.
Validate extreme cases such as zero-current or large-load scenarios to ensure results make physical sense, strengthening the reliability of your calculations.

6. Common Pitfalls & Misconceptions

Assuming terminal p.d. equals e.m.f. during current flow leads to overestimating circuit performance. Only ideal power supplies behave this way; real ones suffer internal losses.
Confusing resistance values by treating internal resistance as negligible when it is actually significant results in wrong current and voltage predictions.
Misapplying Ohm’s law by using the total resistance in place of the load resistance when computing terminal p.d. yields incorrect voltage distributions.
Ignoring lost volts often causes students to overlook where the missing energy goes, but internal heating must always be included in energy accounting.

7. Connections & Extensions

Links to power calculations arise because terminal p.d. directly determines the useful power delivered to external components, while lost volts account for internal heating.
Battery efficiency analysis depends on comparing terminal p.d. to e.m.f., providing insight into how much of the source’s energy is actually delivered to the load.
Circuit design considerations rely on selecting components that minimize internal resistance effects, especially in high-current applications like motors or in low-power electronics.
Experimental determination of internal resistance uses the linear relationship between terminal p.d. and current, bridging theoretical concepts with practical measurement methods.

E.M.F. vs. Terminal Potential Difference

Summary

1. Definition & Core Concepts

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

7. Connections & Extensions

E.M.F. vs. Terminal Potential Difference

Summary

1. Definition & Core Concepts

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

Comparison Table

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

7. Connections & Extensions

Comparison Table