Aug 13, 2024

**Capacitor Demonstration**:- 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).

**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.

**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 ).

**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.

- 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.