OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Internal resistance: (i) the equations E = I ( R + r ) and E = V + I r
A real source of e.m.f. has internal resistance r, so some energy per unit charge is dissipated inside the source.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 3 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A real source of e.m.f. has internal resistance r, so some energy per unit charge is dissipated inside the source. The e.m.f. E equals the total potential difference per unit charge around the circuit: E = I(R + r), where R is the external resistance and I the current. The terminal potential difference V is the p.d. across the external resistance only, so V = IR. Substituting gives E = V + Ir, showing that V is less than E whenever current flows, and that V equals E only when I = 0, as on open circuit. The lost volts Ir increase with current. Rearranging, r = (E − V)/I, which is the basis of the experimental determination of internal resistance.
What earns the marks
- States that E = I(R + r) applies to the whole circuit, with R the external resistance and r the internal resistance.
- Explains that V = IR is the terminal p.d. across the external resistance only.
- Derives E = V + Ir by substituting V = IR into E = I(R + r).
- States that V equals E only when the current is zero, for example on open circuit.
- Identifies Ir as the lost volts and explains that V falls as I increases.
- Rearranges to r = (E − V)/I for use in experimental determination.
Common mistakes and how to put them right
Treating V as equal to E at all times.
Put it right: V = E − Ir, so V equals E only when I = 0.
Using E = IR and omitting the internal resistance term.
Put it right: The total resistance is R + r, so E = I(R + r).
Confusing e.m.f. with terminal p.d.
Put it right: e.m.f. is the energy transferred per unit charge by the source, while terminal p.d. is the energy transferred per unit charge in the external circuit.
Assuming r is always negligible.
Put it right: r is a property of the source and becomes significant when the current is large.
Exam tips
- Write the two equations side by side and show the substitution step explicitly when asked to derive E = V + Ir.
- Check the rearrangement algebraically before substituting numbers, especially when making r the subject.
- Use the open-circuit condition I = 0 to justify any statement that V equals E.
Try the lesson
The start of the Internal resistance: (i) the equations E = I ( R + r ) and E = V + I r lesson, made from checked teaching notes for this specification point.
Listen
A real source of e.m.f. has internal resistance r, so some energy per unit charge is dissipated inside the source. The e.m.f. E equals the total potential difference per unit charge around the circuit: E = I(R + r), where R is the external resistance and I the current. The terminal potential difference V is the p.d. across the external resistance only, so V = IR. Substituting gives E = V + Ir, showing that V is less than E whenever current flows, and that V equals E only when I = 0, as on open circuit. The lost volts Ir increase with current. Rearranging, r = (E − V)/I, which is the basis of the experimental determination of internal resistance. A strong answer earns marks for these points. States that E = I(R + r) applies to the whole circuit, with R the external resistance and r the internal resistance. Explains that V = IR is the terminal p.d. across the external resistance only. Derives E = V + Ir by substituting V = IR into E = I(R + r). States that V equals E only when the current is zero, for example on open circuit. A common slip: Treating V as equal to E at all times. Instead, V = E − Ir, so V equals E only when I = 0. Exam tip: Write the two equations side by side and show the substitution step explicitly when asked to derive E = V + Ir.
Key words
Say what each word means before you turn the card.
Electromotive force and internal resistance
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Terminal potential difference and lost volts
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Circuit equations and algebraic rearrangement
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Energy transfer per unit charge in a source
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See every definition
- Electromotive force and internal resistance
- A real source of e.m.f. has internal resistance r, so some energy per unit charge is dissipated inside the source.
- Terminal potential difference and lost volts
- The terminal potential difference V is the p.d. across the external resistance only, and the lost volts Ir increase with current.
- Circuit equations and algebraic rearrangement
- Substituting V = IR into E = I(R + r) gives E = V + Ir, and rearranging gives r = (E − V)/I.
- Energy transfer per unit charge in a source
- E.m.f. is the energy transferred per unit charge by the source, while terminal p.d. is the energy transferred per unit charge in the external circuit.
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