Determining EMF and r from a V-I Graph

Electrical Circuits - OCR A-Level Physics

From V = EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). - Ir, this has the form $y = mx + c. Plot terminal p.d. (V)$ on the y-axis against 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). (I) on the x-axis.

The y-intercept gives the electromotive forceThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). by a source in driving chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). 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).).
The gradient equals -r (negative of internal resistanceThe opposition to currentThe rate of flow of charge. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of charge. Measured in amperes (A).. Measured in ohms (Ω).The resistanceThe opposition to current 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.).
The line slopes downward because V falls as I increases.
Use a variable resistor to change I and record V for each value.

\begin{aligned} V &= \varepsilon - Ir \quad \Rightarrow \quad \text{gradient} \\ &= -r, \quad y\text{-intercept} \\ &= \varepsilon \end{aligned}

V-I graph for determining EMF and internal resistance

Straight line with positive y-intercept (labelled EMF) and negative gradient (labelled -r). V on y-axis, I on x-axis.

Examiner Tips and Tricks

In OCR practical questions, you may be asked to 'describe an experiment' to find EMF and r.
State: vary R (or use a potentiometerA potential divider with a sliding contact that allows continuous variation of the output voltageThe energy transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference. from zero to the supply voltageThe energy transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference..), record V and I for at least six values, plot V against I, read intercept for EMF and gradient for -r.

Common Mistake MEDIUM

Wrong: Stating the gradient is r (positive).
Right: The gradient is -r (negative). Internal resistance is a positive value, so $r = magnitude$ of the gradient.