Discharging a capacitor
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Describe the shape of the voltage vs. time graph for a capacitor discharging through a resistor. What does the shape represent?
The voltage vs. time graph is a decreasing exponential curve. This represents the voltage decreasing over time as the capacitor discharges its stored charge through the resistor.
Define the term 'time constant' (τ) for a capacitor discharging through a resistor. What does it physically represent?
The time constant (τ) is the time taken for the voltage (or current, or charge) to fall to approximately 37% (1/e) of its initial value during the discharge of a capacitor. It is given by the formula τ = RC.
State the formula that relates the voltage (V) across a discharging capacitor to its initial voltage (V₀), time (t), resistance (R), and capacitance (C).
The voltage across a discharging capacitor is given by: V = V₀e^(-t/RC), where V₀ is the initial voltage, t is time, R is resistance, and C is capacitance.
A 100μF capacitor discharges through a 10kΩ resistor. Calculate the time constant (τ) of the circuit.
The time constant (τ) is calculated as τ = RC. Therefore, τ = (10,000 Ω) * (100 × 10⁻⁶ F) = 1 second.
If a capacitor initially charged to 12V is discharging through a resistor, what is the voltage across the capacitor after one time constant (τ)?
After one time constant, the voltage is approximately 37% of its initial value. Therefore, V = 0.368 * 12V ≈ 4.42V.
How does increasing the resistance in a discharging RC circuit affect the discharge time and the time constant?
Increasing the resistance increases the discharge time because it limits the current flow. The time constant τ = RC is directly proportional to R, so increasing R increases τ, meaning a longer time to discharge.
How does increasing the capacitance in a discharging RC circuit affect the discharge time and the time constant?
Increasing the capacitance increases the discharge time because the capacitor can store more charge. The time constant τ = RC is directly proportional to C, so increasing C increases τ, meaning a longer time to discharge.
Write the equation to describe how the charge (Q) on a discharging capacitor varies with time.
The charge (Q) on a discharging capacitor varies with time according to the equation: Q = Q₀e^(-t/RC), where Q₀ is the initial charge, t is the time, R is the resistance, and C is the capacitance.
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