Determining Internal Resistance (OCR A Level Physics)

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

Variables

• Independent variable = resistance, R (Ω)
• Dependent variable = voltage, V (V) & current, I (A)
• 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

ε = I (R + r)

• Where:
  • ε = 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:

ε = IR + Ir = V + Ir

• Rearranging this equation for V:

V = –rI + ε

• Comparing this to the equation of a straight line: y = mx + c
  • y = V (V)
  • x = I (A)
  • Gradient = –r (Ω)
  • Y-intercept = ε (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 burning is smelled
• Make sure there are no liquids close to the equipment, as this could damage the electrical equipment

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