Initial test with a light bulb showed no effect because the capacitor was not charged.
When charged with a battery, the capacitor can light up the bulb.
Concept of Stored Energy:
Capacitors not only store charge but also energy.
Charged capacitors have separated charges that desire to recombine, leading to energy release when the circuit is completed (light/heat from the bulb).
Understanding Electrical Potential Energy
Energy Calculation for Capacitors:
Formula for electrical potential energy: ( \Delta U = Q \times V )
Expected energy for capacitors: ( Q \times V )
Actual energy stored in a capacitor: ( \frac{1}{2} Q \times V )
Reason for the Factor of 1/2:
Not all charges drop through total initial voltage during discharge.
As charges are transferred, the voltage decreases as the total charge reduces.
On average, charges drop through only half the initial voltage.
Formulas for Energy in Capacitors
Energy Formula Variants:
( E = \frac{1}{2} Q \times V )
( E = \frac{1}{2} C \times V^2 )
Capacitance (C): charge (Q) divided by voltage (V)
Memory Aid:
Formula with 'C' includes ( V^2 ), without 'C' does not have ( V^2 ).
Practical Considerations
Voltage Considerations:
Voltage in formulas refers to the voltage across the capacitor, not necessarily the battery's voltage.
Example: 9-volt battery charging a capacitor with 4 coulombs leads to 18 joules of stored energy.
Complex Circuits:
In circuits with multiple batteries and capacitors, calculate energy using the specific voltage across each capacitor.
Example Calculation: 5 coulombs charge on a capacitor results in 7.5 joules.
Conclusion
Understanding the function and energy storage capabilities of capacitors is essential, particularly in varied circuit configurations.
Accurate calculations require attention to the voltage across the specific capacitor in question.