discharging capacitors

• equipment

  • electrolutic capacitor
  • resistor
  • battery
  • voltmeter
  • switch
• method

  • set up apparatus
  • set switch to A position and allow capacitor to fully charge
  • move switch to B position and start stopwatch
  • record voltage reading at t=0 and at 5s intervals until 120s have passed
  • repeat experiment twice more and obtain average voltage at each time
  • experiment can be repeated for different resistors or capacitors to see how time constant varies
• graphs and calculations

  • calculate natural logarithms of voltage at each time and tabulate
  • plot graph of lnV against time and draw line of best fit
  • straight line graph with negative gradient
  • decay of voltage across capacitor is exponential
  • gradient = $-\frac{1}{RC}$
  • $V=$$V_0e^{-\frac{t}{RC}}\ \ \rightarrow\ \ \ln\left(V\right)=$$-\frac{1}{RC}t+$$\ln\left(V_0\right)$
  • if capacitance is known you can find the time constant using RC and compare with the graph value
• safety

  • if voltage goes too high battery can explode and release harmful chemicals

  precautions

  • ensure capacitor is connected with correct polarity and its voltage rating exceeds voltage of battery
• improvements

  • can plot graph of voltage against time to show exponential decay
  • time constant can be found by finding time when voltage is 37% of the original voltage