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

• Electrical components can get hot when used for a long period
• Switch off the power supply right away if there is a burning smell
• Make sure there are no liquids close to the 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