Topic 4 - Capacitors Flashcards
Chapters 6 & 7 (32 cards)
What is a capacitor?
Stores energy in its electric field, whereas an inductor stores energy in its magnetic field. It consists of two conducting plates, separated by an insulator.
What is an RC circuit?
Resistor - Capacitor circuit.
How is charge stored in the capacitor? What are the properties of the charge?
One plate will have positive charge (+q), and the other plate negative (-q). Charge is equal in magnitude, and the amount of charge is proportional to voltage.
What is the constant of proportionality for charge to voltage across a capacitor?
Capacitance - C
Measured in Farads, which is Coulombs/Volts.
Capacitance formula for a parallel-plate capacitor?
Where A is the surface area of each plate, d is the distance between the plates, and e is the permittivity of the dielectric. - Higher permittivity = higher capacitance
Which leg of a capacitor does a curved line represent?
Shorter leg, negative
What is the equation for the current through a capacitor?
Current is the capacitance x the derivative of voltage with respect to time.
What happens when the voltage across a capacitor stays constant?
Rate of change is zero, as V is constant. Capacitor becomes an open circuit, as i = 0.
Ideal vs Real capacitors?
Ideal capacitors don’t dissipate energy. Energy is absorbed from a circuit, stored as electric field and then released back to the circuit.
Real capacitors have a resistor (very high resistance, MΩs) connected in parallel, called a leakage resistance, resulting in a slow loss of stored energy internally.
What is the capacitance of capacitors in parallel?
You can add them together into one big capacitor. Different to resistors, as resistors must be in series.
What is the capacitance of capacitors in series?
Same as resistors in parallel.
What is the formula for energy stored within a capacitor?
What is the formula for power delivered to the capacitor?
i = C dv/dt
What is a circuit response?
If a capacitor experiences a different voltage/current, it will charge or discharge accordingly. This is called a circuit response.
Types of circuit responses?
Natural response - The circuits behaviour when the external power source is removed, causing all stored charge in the capacitor to discharge through the resistor over time.
Forced response - When external sources change the voltage/current being applied to the circuit. It is the transient response.
What is the transient period?
The time during which the voltage across the capacitor is changing, accumulating charge.
What is the final result after solving the differential equation for the natural response of a circuit?
-C dv/dt = v/r
What is the differential equation that models the natural response of a circuit?
Using KCL:
-C dv/dt = v/r
What is the time constant?
The time constant is the time required for the circuit response to decay to 1/e (or 36.8%) of it’s initial value OR increase to 1-1/e (or 63.2%) of its final value.
How many time constants does it take for an RC circuit to finish its response?
It takes 5, to reach its final state (fully charged) or stable state (fully discharged). Therefore, a smaller time constant (tau) will be a faster response, and a bigger (tau) will be a slower response.
How is the time constant denoted? What are its expressions?
It is denoted by tau (τ). The speed at which voltage decays depends on the coefficient of t, which is (-1/τ). To find the time constant (τ), τ = Resistance x Capacitance.
What are the steps in calculating the natural response of an RC circuit?
- Find initial voltage (vo) of the capacitor before connected to the resistor
- Find τ by τ = RC. AFTER t=0. R = Rth, capacitors can be treated as open circuits.
When do capacitors act as an open circuit?
The capacitor acts as an open circuit when it is in a steady state. (No current flowing into capacitor, switch has been closed for a while.)
What is the initial voltage in a step response circuit?
Even though the circuit is externally forced a different voltage/current, since voltage of a capacitor cannot change instantaneously, voltage before and after the switch is opened/closed = Vo.
