4.3.7 Circuits with Multiple Sources of e.m.f

• More complex circuit problems may include circuits with two or more sources of e.m.f
  • This is often from multiple cells

• Cells can also be connected in series or parallel
• The total voltage of the combined cells can be calculated in the same way as voltage
  • If the cells are connected in series, the total voltage between the ends of the chain of cells is the sum of the potential difference across each cell
  • If the cells are connected in parallel, the total voltage across the arrangement is the same as for one cell

• The important part is making sure current flowing in one direction (from positive to negative) is taken as positive and the current flowing in the opposite direction as negative

Aims of the Experiment

• The aim of the experiment is to investigate circuits with more than one source of e.m.f (batteries)
• The total potential difference measured in a series and parallel circuit should be similar to the calculated total potential difference of the circuit

Variables:

• Independent variable = Potential difference of the cells, V_total
• Dependent variable = Potential difference of the resistor, V

Equipment List

• Cells
• Leads
• Voltmeter
• Resistor

• Resolution of measuring equipment:
  • Voltmeter = 0.1 V

Method

1. Set up a circuit with two cells in series. They can be of any voltage but preferably low (eg. 5 V) with a fixed resistor. Connect a voltmeter around the resistor
2. Record the voltage across the resistor, as the resistor is the only
   component this will be the potential difference supplied by the cells
3. Swap at least one of the cells to one with a higher voltage
4. Record the reading on the voltmeter again
5. Repeat this for 3-5 voltage readings for the resistor
6. Set up a circuit now with the two cells in parallel. Still, connect a voltmeter around the resistor
7. Record the voltage across the resistor
8. Replace the batteries with two batteries with a different voltage, still in parallel. They both must have the same voltage
9. Repeat the experiment for 3-5 voltage readings for the resistor

Analysis of Results

• The expected combined potential difference (p.d) for each battery combination is calculated by the following:
  • In series: Combined p.d is the sum of their individual voltages

V_total = V₁ + V₂ + ... V_n for n sources of e.m.f

• • In parallel: Combined p.d is the same as the p.d of each battery

• Compare the results of the p.d across the resistor to its expected combined p.d

• In parallel, the resistor will have the same p.d as the batteries because their terminals are at the same point. Therefore, the potential between those two points are still the same
• The 2 batteries connected in parallel should not be different voltages
  • The one with the higher voltage will discharge into the one of lower until they are equal which can cause wires to be burnt, creating sparks when connecting the cells
  • This can cause overheating and failure of both batteries

Evaluating the Experiment

Systematic Errors:

• Make sure the voltmeter starts from 0, to avoid a zero error

Random Errors:

• The internal resistance of the cells will affect the reading on the voltmeter, so the p.d calculated may not be exactly as predicted
• If the circuit is not disconnected between each reading, the resistance of the components could be affected by the temperature rise in the components
• Repeat readings over a wide range of voltages will produce a more reliable result

Safety Considerations

• When there is a high current, and a thin wire, the wire will become very hot. Make sure never to touch the wire directly when the circuit is switched on
• 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
• The components will get hot especially at higher voltages. Be careful when
  handling them
• Disconnect the power supply in between readings to avoid the components heating up too much