# 5.4.2 Required Practical: Investigating EMF & Internal Resistance

### Required Practical: Investigating EMF & Internal Resistance

#### Aims of the Experiment

The overall aim of the experiment is to investigate the relationship between e.m.f and internal resistance by measuring the variation of current and voltage using a variable resistor

• Independent variable = voltage, V (V) & current, I (A)
• Dependent variable = resistance, R (Ω)
• Control variables:
• E.m.f of the cell
• Internal resistance of the cell

#### Equipment List • Resolution of measuring equipment:
• Voltmeter = 1 mV
• Ammeter = 0.1 mA

#### Method 1. The cell and the resistor, labelled r, should be connected in series and considered to be a single cell
2. With the switch open, record the reading V on the voltmeter
3. Set the variable resistor to its maximum value, close the switch and record V and the reading I on the ammeter – make sure to open the switch between readings
4. Vary the resistance of the variable resistor up to a minimum of 8-10 readings and record values for V and I for each resistance. Ensure to take readings for the whole range of the variable resistor
• An example of a suitable table might look like this: #### Analysing the Results

• The relationship between e.m.f. and internal resistance is given by

E = I (R + r)

• Where:
• E = electromotive force (V)
• I = current (A)
• R = resistance of the load in the circuit (Ω)
• r = internal resistance of the cell (Ω)

• This can be simplified into the form:

E = IR + Ir = V + Ir

• Rearranging this equation for V:

V = –rI + E

• Comparing this to the equation of a straight line: y = mx + c
• y = V (V)
• x = I (A)
• Gradient = –r (Ω)
• Y-intercept = E (V)

1. Plot a graph of V against I and draw a line of best fit
2. Measure the gradient of the graph and compare it with the manufacturer’s value of the resistor
3. The y-intercept will be the e.m.f and the gradient will be the negative internal resistance: #### Evaluating the Experiment

Systematic Errors:
• Only close the switch for as long as it takes to take each pair of readings
• This will prevent the internal resistance of the battery or cell from changing during the experiment
Random Errors:
• Only use fairly new cells otherwise the e.m.f. and internal resistance of run-down batteries can vary during the experiment
• Wait for the reading on the voltmeter and ammeter to stabilise (stop fluctuating) before recording the values
• Take multiple repeat readings (at least 3) for each voltage and current and calculate a mean to reduce random errors

#### Safety Considerations

• This is a very safe experiment, however, electrical components can get hot when used for a long period
• Switch off the power supply right away if you smell burning
• Make sure there are no liquids close to the equipment, as this could damage the electrical equipment

#### Worked Example

In an experiment, a student uses a variable resistor as an external load. The current flowing through the circuit is measured with a suitable milliammeter and the potential difference across the variable resistor is measured with a voltmeter for a range of resistance values.

The data collected was as follows: Plot a graph of these results and determine the e.m.f. and the internal resistance directly from the graph.

Step 1: Plot the data on a graph of V against I and draw a line of best fit Step 2: Draw the largest triangle possible in order to calculate the gradient  Step 3: Determine the e.m.f. and the internal resistance from the graph

V = –rI + E

• From this equation:
• Gradient = –r (Ω)
• Y-intercept = E (V)
• Therefore:
• Internal resistance, r = 22.7 Ω
• E.m.f. E = 1.60 V ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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