9702 · 19.3
Discharging a capacitor flashcards
Revision flashcards for Cambridge 9702 Discharging a capacitor (syllabus 19.3). Flip, recall, then mark a real past-paper question.
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What type of decay do charge, voltage, and current exhibit during capacitor discharge?
Exponential decay.
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What is the formula for the time constant (τ) of an RC circuit?
τ = RC (Resistance × Capacitance).
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What does V₀ represent in the discharge equation Vc = V₀ e⁻ᵗ/τ?
The initial voltage across the capacitor at the start of discharge (t=0).
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What percentage of its initial value does the charge on a discharging capacitor fall to after one time constant?
Approximately 37% (or 1/e).
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How does the rate of discharge relate to the remaining charge in a capacitor?
The rate of discharge is directly proportional to the amount of charge still held by the capacitor.
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What happens to the current as a capacitor discharges?
The magnitude of the current decreases exponentially over time.
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State the formula for energy stored in a capacitor.
E = ½QV or E = ½CV².
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What is the approximate value of 1/e?
0.368 (or 36.8%).
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How is capacitance (C) defined?
C = Q/V (Charge per unit voltage).
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What does the time constant (τ) measure?
A measure of how quickly the capacitor discharges. It's the time taken for charge/voltage/current to fall to 37% of its initial value.
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How can you linearize the capacitor discharge equation V = V₀ e⁻ᵗ/RC?
By taking the natural logarithm of both sides to get ln(V) = -(t/RC) + ln(V₀).
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In a graph of ln(V) versus t for a discharging capacitor, what does the gradient represent?
The gradient is equal to -1/τ or -1/RC.
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What is the half-life (t₁/₂) of a discharging capacitor?
The time taken for the charge, voltage, or current to fall to half of its initial value.
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What is the relationship between the half-life (t₁/₂) and the time constant (τ)?
t₁/₂ = τ ln(2) ≈ 0.693τ.
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How does the energy stored in a discharging capacitor change with time?
It also decays exponentially, but faster than charge or voltage, following the equation E = E₀ e⁻²ᵗ/τ.
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Why does energy decay faster than voltage in a discharging capacitor?
Because energy is proportional to the square of the voltage (E ∝ V²). Since V decays as e⁻ᵗ/τ, V² (and thus E) decays as (e⁻ᵗ/τ)² = e⁻²ᵗ/τ.