Circuits Containing Capacitors & Resistors (OCR A Level Physics)

Circuits Containing Capacitors & Resistors

• Rearrange the capacitor equation to make charge, Q the subject:

• The capacitance C of a capacitor is fixed

  • It is determined during the manufacturing process

• Hence, charge Q is directly proportional to potential difference V 

Investigation with a test circuit

• The relationship between the potential difference across a capacitor and the charge stored on it can be investigated experimentally by charging a capacitor using a constant current

• A suitable test circuit contains:

  • a parallel plate capacitor 

  • a switch

  • a battery

  • an ammeter connected in series with the capacitor

  • a variable resistor

  • a voltmeter connected in parallel with the capacitor

Test circuit to charge a capacitor

The potential difference across a capacitor and the charge stored on a capacitor is investigated using this test circuit 

• Close the switch and constantly adjust the variable resistor to keep the charging current at a constant value for as long as possible

  • This will be impossible when the capacitor is close to fully charged

• Record the potential difference across the capacitor at regular time intervals until it equals the potential difference of the power supply

• Plot a graph of charging current and time taken to charge

  • Once the capacitor is fully charged the current passing through it drops to zero

Graph of charging current and time using test circuit

The current-time graph of the capacitor in the test circuit whilst constantly adjusting the variable resistor

• Recall the equation for charge, current and time:

• Use it to calculate the charge stored on a capacitor at a given time

• Then plot a graph of the charge stored Q against the potential difference at each recorded time interval

Graph of potential difference and charge stored

The charge-potential difference graph of a capacitor is a straight line through the origin 

• The calculated charge-potential difference graph is a straight line through the origin

  • Hence, Q and V are directly proportional

  • The gradient of the graph  is constant and equal to the given capacitance of the capacitor, C

  • So,

Investigating Capacitors in Series & Parallel

Aim of the Experiment

• The aim of this experiment is to determine the capacitance of capacitors connected in series and parallel combinations

Variables

• Independent variable = potential difference, V

• Dependent variable = charge, Q

• Control variables:

  • Current in the circuit

  • E.m.f. of the supply

  • Capacitance of each capacitor

Equipment List

• Resolution of measuring equipment:

  • Voltmeter = 0.1 V

  • Ammeter = 0.1 A

  • Stopwatch = 0.01 s

Method

• Set up three circuits: 

  • Circuit 1: single capacitor

  • Circuit 2: capacitors in parallel

  • Circuit 3: capacitors in series

1. Close the switch to charge the capacitor and start the stopwatch

2. As the capacitor charges, record the value of the fixed current and adjust the variable resistor to ensure the current remains constant

3. Record the potential difference and the time since closing the switch in a table

4. Repeat the procedure for circuits 2 and 3

• An example table might look like this:

Analysing the Results

• The relationship between charge, potential difference and capacitance is

• Where:

  • Q = charge across the capacitor (C)

  • V = potential difference across the capacitor (V)

  • C = capacitance of the capacitor (F)

• The total capacitance of each combination of capacitors can be found by

  • plotting a graph of Q against V

  • drawing a line of best fit

  • calculating the gradient, which is equal to:

• The expected results are:

1. The total capacitance of the parallel combination is greater than the capacitance of the series combination

2. If the capacitors have the same capacitance, the combined capacitance of the parallel combination is double the capacitance of one

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3. If the capacitors have the same capacitance, then the combined capacitance of the series combination is half the capacitance of one capacitor

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Evaluating the Experiment

Systematic Errors:

• If a digital voltmeter is used, wait until the reading is settled on a value if it is switching between two

• If an analogue voltmeter is used, reduce parallax error by reading the p.d. at eye level to the meter

• Before closing the switch, check that the voltmeter and ammeter readings start at zero to avoid a zero error

Random Errors:

• Use a data logger to record the potential difference and current. This will allow for calculations of charge in real-time and for graphs of charge against p.d. to be plotted in real-time

• When plotting graphs, only use the values for which the current is approximately constant as it will be difficult to keep the current constant once the capacitor is fully charged

Safety Considerations

• Keep water or any fluids away from the electrical equipment

• Make sure no wires or connections are damaged

• Capacitors can still retain charge after the power supply is removed which could cause an electric shock

  • These should be fully discharged and removed after a few minutes