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EMF and internal resistance calculator

A-level Electricity

The emf of a cell is the terminal p.d. plus the p.d. lost across its internal resistance.

ε = V + I r

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

11.0 V

Working

  1. Write the equation
    ε = V + I r
  2. Rearrange to make V the subject
    V = ε − I r
  3. Substitute the values
    V = 12 − 2 × 0.5
  4. Calculate
    V = 11 V
  5. Give the answer to 3 significant figures
    V = 11.0 V

Worked example

Find V, the terminal potential difference. Given: emf ε = 12.0 V; current I = 2.00 A; internal resistance r = 0.500 Ω.

  1. Write the equation
    ε = V + I r
  2. Rearrange to make V the subject
    V = ε − I r
  3. Substitute the values
    V = 12 − 2 × 0.5
  4. Calculate
    V = 11 V
  5. Give the answer to 3 significant figures
    V = 11.0 V

Symbols and units

SymbolQuantitySI unit
εEmfV
VTerminal potential differenceV
ICurrentA
rInternal resistanceΩ

EMF and internal resistance: rearranged

  • To find emf: ε = V + I r
  • To find terminal potential difference: V = ε − I r
  • To find current: I = (ε − V) / r
  • To find internal resistance: r = (ε − V) / I

Exam tip

The “lost volts” are Ir. The terminal p.d. drops as the current drawn from the cell increases.

Common questions

What is the formula for emf and internal resistance?

The equation is ε = V + I r, where ε is the emf (V); V is the terminal potential difference (V); I is the current (A); r is the internal resistance (Ω).

What units should I use for emf and internal resistance?

In SI units: emf in V, terminal potential difference in V, current in A, internal resistance in Ω. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange ε = V + I r?

Rearranging gives these forms: to find emf: ε = V + I r. to find terminal potential difference: V = ε − I r. to find current: I = (ε − V) / r. to find internal resistance: r = (ε − V) / I.

Practise emf and internal resistance questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

Read the full explanation on the Battery internal resistance formula page. More electricity equations: Charge, current and time, Ohm’s law, Electrical power, Electrical power, Energy transferred, Resistors in series, Resistors in parallel, Resistivity. See the full list on the a-level physics equation calculator page.