AP Physics 2- 10.7 Conservation of Electric Energy- Study Notes- New Syllabus
AP Physics 2- 10.7 Conservation of Electric Energy – Study Notes
AP Physics 2- 10.7 Conservation of Electric Energy – Study Notes – per latest Syllabus.
Key Concepts:
- Conservation of Electric Energy
Conservation of Electric Energy
The total electric energy in a closed system is conserved. Energy can be transformed between different forms, but the total remains constant.
In the context of capacitors and electric circuits, electric potential energy can be converted into:
- Kinetic energy of charges (current flow)
- Heat energy (Joule heating in resistors)
- Electromagnetic energy (radiation)
Energy stored in capacitors is part of the electric energy that can be transferred or transformed but not lost overall.
Key Equations:
Electric potential energy stored in a capacitor:
\( U = \dfrac{1}{2} C V^2 = \dfrac{Q^2}{2C} = \dfrac{1}{2} Q V \)
Work done by electric forces in moving charges:
\( W = \Delta U = q \Delta V \)
For a system with multiple energy transformations:
\( U_{initial} + K_{initial} + … = U_{final} + K_{final} + … \)
Properties:
- Electric energy can neither be created nor destroyed; it only changes form.
- In circuits, the energy stored in capacitors can be completely converted to kinetic energy of charges or dissipated as heat, depending on the configuration.
- In electrostatics, the work done to assemble charges equals the electric potential energy stored in the system.
Example :
A 10 μF capacitor is charged to 12 V and then connected across a 100 Ω resistor. Find the total energy initially stored in the capacitor and explain how this energy is conserved when the capacitor discharges.
▶️ Answer/Explanation
Step 1: Energy stored in the capacitor: \( U = \dfrac{1}{2} C V^2 \)
= \( 0.5 \times 10 \times 10^{-6} \times 12^2 \)
= \( 7.2 \times 10^{-4} \, J \)
Step 2: When the capacitor is connected across the resistor, the stored electric energy is transformed into heat energy in the resistor (Joule heating).
Step 3: Conservation of energy: The total energy remains the same; it is just converted from electric potential energy to thermal energy in the resistor. No energy is lost; it only changes form.
Answer: Total initial energy = 0.72 mJ, which is fully converted to heat energy during discharge.
Example :
A 5 μF capacitor is charged to 10 V and then connected across a resistor. Find the total energy initially stored in the capacitor.
▶️ Answer/Explanation
Formula: \( U = \dfrac{1}{2} C V^2 \)
= \( 0.5 \times 5 \times 10^{-6} \times 10^2 \)
= \( 2.5 \times 10^{-4} \, J \)
Answer: Energy initially stored = 0.25 mJ. This energy can be fully converted to heat in the resistor.