Topic 2 of 4

Energy per charge

Potential difference describes energy transferred per charge between two points. A source's e.m.f. describes the energy it supplies per charge, including energy subsequently transferred inside the source.

If electrical work W is done as charge Q passes through a load, the potential difference across its named terminals is:

V = W/Q or W = VQ
1 V = 1 J/C = kg m² s^-3 A^-1

A load transferring 24.0 J as 4.00 C passes has p.d. 24.0/4.00 = 6.00 V. That is 6.00 J transferred for each coulomb, not 6.00 J regardless of how much charge passes. Current is through a section; voltage is between two points.

A potential level needs a reference

Electric potential is electric potential energy per unit positive test charge, relative to a chosen reference. Suppose point Q is assigned V_Q = 0 and point P has V_P = +6 V. Their p.d. is V_P - V_Q = 6 V. For a positive test charge in the given field, this represents a 6 J/C difference in electric potential energy.

Assigning Q a value of +10 V and P a value of +16 V leaves that difference unchanged. Adding the same constant to both potential levels changes the reference, not the p.d. A voltmeter compares its two connection points; it does not report a potential level without a reference.

What a source supplies

Electromotive force, or e.m.f., is the energy a source supplies to the circuit per unit charge through it, by converting another form of energy into electrical energy. It is measured in volts, despite the word force. It is not a mechanical force measured in newtons.

E.m.f. ε = source energy supplied / charge

For example, a discharging cell converts chemical energy. Some energy can be transferred internally before the remainder reaches the external circuit. Its terminal p.d. can therefore be lower than its e.m.f. The symbol ε is used here for e.m.f.; E is also used for it in circuit equations. Define the quantity locally so it is not confused with electric field strength or total energy.

Worked source account

Keep the source and external boundaries distinct

A steady discharging source has e.m.f. 1.60 V, terminal p.d. 1.50 V and current 0.400 A. The source converts 1.60 J per coulomb; 1.50 J per coulomb reaches the external circuit and 0.10 J per coulomb is transferred internally.

Separate conversion inside the source from delivery to the load

For the same steady current, I = 0.400 A, the source e.m.f. is 1.60 V and its terminal p.d. is 1.50 V. All bars use the same power scale. They show energy rates, not current or voltage arrows.

For each coulomb passing through the source, 1.60 J is supplied, 0.10 J is transferred internally and 1.50 J reaches the external circuit. Current continues through the load.

The total source conversion divides into external terminal output and internal transfer. The three labelled powers form one energy account at the same current; the e.m.f. and terminal p.d. describe different energy transfers per charge.

Current 0.400 A means 0.400 C passes each second. Multiplying each energy-per-charge value by that rate gives:

One steady source: energy per charge and the corresponding power
Transfer	J per C	Power / W
Total source conversion	1.60	0.640
External circuit	1.50	0.600
Inside the source	0.10	0.040

0.640 W = 0.600 W + 0.040 W

The e.m.f. and terminal p.d. are supplied here; the account does not require an internal-resistance calculation. A voltmeter across the external load measures its p.d., not automatically the source's total energy conversion per charge.

The power equations express these energy-per-charge and charge-per-time ideas directly.

Optional check A discharging source has e.m.f. 1.60 V, terminal p.d. 1.50 V and steady current 0.400 A. Which power account is consistent with these readings?