Edexcel A Level Physics:复习笔记7.10 Energy Stored by a Capacitor

• The energy stored by a capacitor is given by:

• Substituting the charge Q with the capacitance equation Q = CV, the energy stored can also be calculated by the following equation:

• By substituting the potential difference V, the energy stored can also be defined in terms of just the charge stored Q and the capacitance, C:

Step 1: Write down the equation for energy stored, in terms of C and V and list the known values

Capacitance, C = 1500μF

Final p.d, V2 = 30 V

Initial p.d V1 =10 V

Step 2: The change in energy stored in proportional to the change in p.d

Step 3: Substitute in the values

• The charge stored Q on the capacitor is given by the equation Q = CV
  • Therefore, the charge stored Q is directly proportional to the potential difference across the plates V
• The graph of charge against potential difference is therefore a straight line graph through the origin
• The gradient of the graph represents the capacitance C, which is a constant
• The electrical (potential) energy stored in the capacitor can be determined from the area under the potential-charge graph which is equal to the area of a right-angled triangle:

Area =  × base × height

The area under a potential difference-charge graph represents the energy stored by a capacitor

• Therefore the work done, or energy stored W in a capacitor is defined by the equation:

• Where:
  • W = energy stored (J)
  • Q = charge stored (C)
  • V = potential difference across the plates (V)

   

Step 1: Determine the charge on the sphere at the potential of 100 kV

• • From the graph, the charge on the sphere at 100 kV is 1.8 μC

Step 2: Calculate the electric potential energy stored

• • The electric potential energy stored is the area under the graph at 100 kV
  • The area is equal to a right-angled triangle, so, can be calculated with the equation:

• • Substituting in the values gives: