Ch. 7: Capacitors and Inductors Flashcards
Capacitors:
Applications of Capacitors
Block DC current while passing AC
Shift Phase
Store Energy
Suppress Noise
Start Motors
Capacitors:
Properties of
Ideal Capacitors
- When no voltage changing(DC), current = 0
- No current will flow with DC
- (Current will flow for a short time upon voltage changes, which cause charging/discharging)
- Does not dissipate energy, stored energy can be retrieved later
Capacitors:
Difference between
Real and Ideal Capacitors
Ideal capacitors have exactly 0 current flow with static voltage.
Real capacitors have small leakage current.
This can be represented with a parallel leakage model, which places a very high resistance (>100 MΩ) in parallel with the capacitor.
Can typically be ignored.
Capacitors:
Charge within a Capacitor
(q)
q = Cv
where C = capacitance in Farads(F)
Capacitors:
Energy stored
in a Capacitor (w)
ωc = (1/2)Cv2
where C=capacitance in Farads
Energy ωc is measured in Joules (J)
Capacitors:
Capacitor Current-Voltage Relationship
(Differential equation)
The current through a capacitor is proportional to the change in voltage:
i = C dv/dt
or
v(t)= 1/C ∫i(τ)dτ + v(t0)
Capacitors:
Instantaneous Power
delivered to a capacitor
(Differential Equation0
Starting with
p = i*v
Substitute for the current of the capacitor, i:
p = v* Cdv/dt
Capacitors:
Unit of Capacitance
Farad - F
1 F = 1 Coulomb/Volt = 1 amp-sec/volt
Capacitors:
Capacitance of a
Capacitor
Measure how capacitive it is, based on geometry and electrical Permittivity
C = 𝜀A/d
- A - Area of parallel plates
- d - distance between plates
- 𝜀 - Electrical Permittivity of insulating material
Free Space
Electrical Permittivity
𝜀0
𝜀0
= 8.854 pF/m
Capacitors:
Equivalent Capacitance
of
Capacitors in Series
(Similar to resistors in parallel)
The inverse of the sum of inverses of individual capacitances
Ceq = 1 / ∑ 1/Ci
Capacitors:
Capacitance of
two capacitors in series
Ceq = C1C2 / (C1 + C2)
Capacitors:
Equivalent Capacitance of
Capacitors in Parallel
Simply the sum of capacitances:
Ceq = ∑Ci
or
Ceq = C1 + C2 + … + CN
Inductors:
Properties of Ideal Inductors
- If current is constant, voltage across the inductor is 0. Acts like short in a static DC circuit
- Current through the inductor cannot change instantly
- Inductor does not dissipate energy, it stores it
Inductors:
Difference between
Ideal and Real Inductors
Ideal Inductors ignore winding resistance and capacitance.
Real Inductors
Have resistance and capacitance within the windings. Both can typically be ignored.
Capacitance really only matters at high frequencies.
Resistance can be modeled by a small resistor in series with an ideal inductor
