EMF & Internal Resistance

Electrical Circuits - OCR A-Level Physics

Key Definition

internal resistance
The resistance to current flow inside the power supply itself. Symbol: r.

$$\varepsilon = IR + Ir$$

Key Definition

terminal p.d.
The p.d. measured across the terminals of a power supply. Equal to the EMF only when no current flows.

Key Definition

lost volts
The p.d. dropped across the internal resistance of the supply. It represents energy wasted as heat inside the cell. Lost volts = Ir.

$$v = Ir$$

Every real powerThe rate of energy transfer. Measured in watts (W). supply has internal resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω).The resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω). within the source of EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). itself, which causes energyThe capacity to do work. Measured in joules (J). to be dissipated inside the source., r.
The electromotive forceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). (EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V).) is the total energyThe capacity to do work. Measured in joules (J). per unit charge.
Some energy is 'lost' inside the cell as heat (lost $volts = Ir)$.
The rest drives current through the external circuit (terminal p.d. = V).
By Kirchhoff's second lawThe sum of EMFs around any closed loop equals the sum of the products of current and resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). (IR). A consequence of conservation of energyEnergy cannot be created or destroyed, only transferred from one form to another. The total energy of a closed system remains constant..: $EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). = terminal p.d. + lost voltsThe potential difference across the internal resistance of a cell. Equal to Ir.$.

\begin{aligned} \varepsilon &= V + Ir \\ &= IR + Ir \end{aligned}

Rearranging gives the terminal p.d.:

V = \varepsilon - Ir

As current I increases, lost voltsThe potential difference across the internal resistance of a cell. Equal to Ir. Ir increases, so terminal p.d. V falls.
When I = 0 (open circuit), $V = EMF. A voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance. reads$ the full EMF.
When the supply is short-circuited, $V = 0$ and $I = EMF / r$.

Cell with internal resistance circuit diagram

Dashed box containing EMF source and small resistor r in series. External resistor R connected. Labels: V across R, lost volts across r.

Common Mistake MEDIUM

Wrong: Writing $EMF = IR. This ignores$ the internal resistance entirely.
Right: $EMF = IR + Ir. The EMF drives current through BOTH$ the external resistance R AND the internal resistance r.