Charging and Discharging Capacitors Flashcards
What is the equation for the charge on a charging capacitor in a capacitor-resistor circuit?
Q = Q₀(1 - e^(-t/CR))
Where Q₀ is the charge when fully charged, e is the base of the natural logarithm, t is time, C is capacitance, and R is resistance.
What does Q represent in the context of a charging capacitor?
Charge of the capacitor at time t, in coulombs (C)
What is the time constant (τ) in a capacitor-resistor circuit?
τ = CR
It is the time taken for the charge to fall to about 37% of its initial value or rise to about 63% of its final value.
What is the formula for calculating the voltage across a charging capacitor?
V = V₀(1 - e^(-t/CR))
Where V₀ is the potential difference when fully charged.
What is the relationship between current and time in a charging capacitor?
The charging current decreases exponentially over time.
Fill in the blank: The charging time of a capacitor is affected by its _______ and the resistance of the circuit.
capacitance
What happens to the charge on a discharging capacitor over time?
It decreases exponentially according to the equation Q = Q₀e^(-t/CR)
What is the initial charge (Q₀) of a capacitor calculated from its capacitance (C) and voltage (V)?
Q₀ = CV
Where C is capacitance in farads and V is the potential difference in volts.
True or False: The time taken for a capacitor to charge or discharge fully is approximately 5τ.
True
What does the constant-ratio property of exponential relationships indicate?
It takes the same time for a given proportion of charge to be lost, regardless of the initial value.
What is the time taken for a discharging capacitor to decrease to 37% of its charge known as?
Time constant (τ)
How can the time constant (τ) be found from a log-linear graph?
By dividing -1 by the gradient of the line.
Fill in the blank: The time constant for a capacitor is given by τ = _______.
CR
What is the significance of the value of In(2) in the context of capacitor discharge?
It is a constant used in the formula t = -In(2)CR, representing the time to halve the charge.
When is the time constant (τ) considered to be equal to CR?
When calculating the charge of a discharging capacitor.
What type of graph is useful for displaying how charge, potential difference, and current vary over time for a discharging capacitor?
Log-linear graphs
What is the formula for the charge left on a discharging capacitor after time t?
Q = Q₀e^(-t/CR)
What is the effect of increasing resistance (R) in a capacitor-resistor circuit?
The longer it takes to charge or discharge the capacitor.
