The capacitance is the amount of charge stored per volt of potential difference. Due to the equation C = Q/V, the capacitance is measured in coulombs per volt (C/V). 1 coulomb/volt = 1 Farad.
This brings us onto the equation for capacitance:
Q = CV
Where…
- Charge (Q) is measured in coulombs.
- Capacitance (C) is measured in Farads.
- Voltage (V) is measured in volts.
On a graph of of Q = CV, the gradient of the graph is the capacitance with the area under the graph being the energy transferred (work done).
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| Energy Stored in a Capacitor using the graph Q = CV (y = mx) |
- Area of triangle = work done
- =1/2 x base x height
- Work done = 1/2 QV. But, Q = CV.
Therefore, W = 1/2 CV^2 where:
- Work done is energy measured in joules.
- Capacitance in Farads and voltage in volts.
Example
A typical capacitor is 100 micro-Farads. It is charged to 5 volts. What charge is stored by the above pair of values?
- Q = CV = 100×10-6 x 5
- Charge = 5×10-4 Coulombs
What energy is stored?
- Work Done or Energy E = 1/2 x CV^2
- E = 1/2 x 100×10^-6 x 5^2.
- E = 1.25×10^-3 Joules.
Summary
- The charge of a capacitor can be worked out using the equation Charge (Q) = Capacitance (Farads) x Voltage (V).
- The graph of Q against V produces the gradient as the capacitance.
- The area under the graph is the work done or energy. This produces the equation E = 1/2 x CV^2.
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