8. Capacitance A.md
2024-4-11|2024-4-12
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Capacitance
- Dictation/Definition: Define capacitance in the context of an isolated spherical conductor and a parallel plate capacitor. Answer: Capacitance is the ability of a system to charge stored per unit potential difference. For an isolated spherical conductor, it is the charge stored per unit potential created by that charge on the sphere. For a parallel plate capacitor, it is the charge stored per unit voltage across the plates.
- Formula Recall: What is the formula that relates charge (Q), potential difference (V), and capacitance (C)? Answer: .
- Derivation: Using the formula , derive the formula for the combined capacitance of capacitors in series. Answer: For capacitors in series, the total charge Q is the same for each capacitor, but the total voltage V is the sum of the voltages across each capacitor. The combined capacitance is given by .
- Application: How do you derive the capacitance formulae for capacitors in parallel? Answer: For capacitors in parallel, the total capacitance is the sum of the individual capacitances: .
Energy Stored in a Capacitor
- Conceptual Understanding: How can you determine the electric potential energy stored in a capacitor from the potential–charge graph? Answer: The electric potential energy stored in a capacitor is equal to the area under the potential–charge graph.
- Formula Recall: What is the formula for the energy (W) stored in a capacitor in terms of charge (Q) and voltage (V)? Answer: The formula is .
- Alternate Formula: What is the alternate formula for the energy stored in a capacitor in terms of capacitance (C) and voltage (V)? Answer: The alternate formula is .
Discharging a Capacitor
- Graph Analysis: What does the graph of potential difference against time look like for a capacitor discharging through a resistor? Answer: The graph is an exponential decay curve, starting from the initial potential difference and approaching zero as time increases.
- Time Constant: What is the time constant (τ) for a capacitor discharging through a resistor, and how is it calculated? Answer: The time constant τ is the time taken for the quantity (charge, current, or potential difference) to fall to 1/e (approximately 36.8%) of its initial value. It is calculated using τ = RC.
- Discharge Equations: Write the general form of the equation for a quantity x (which could be current, charge, or potential difference) as it changes over time during the discharge of a capacitor through a resistor. Answer: The general form of the equation is , where is the initial value of the quantity.
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