Circuits Containing Capacitors & Resistors (OCR A Level Physics)

• 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,