Chapter 9 Basic Capacitors: Capacitance, RC Circuits, and AC Applications

What is a capacitor?

A fundamental passive electronic component that stores electrical charge.

What are the two main components of a capacitor?

Two conductive plates separated by an insulating material called a dielectric.

What does capacitance measure?

The ability of a capacitor to store charge, defined as C = Q/V.

What is the formula for calculating the charge stored on a capacitor?

Q = CV, where Q is charge, C is capacitance, and V is voltage.

How is energy stored in a capacitor?

In the form of an electric field established by opposite charges on its plates.

What is the formula for the energy stored in a charged capacitor?

W = 1/2 CV^2.

What analogy is used to explain capacitance?

Storing rubber bands in a bottle, where a larger bottle (higher capacitance) can store more rubber bands.

What factors affect capacitance?

Plate area, distance between plates, and dielectric material.

How does plate area affect capacitance?

Capacitance is directly proportional to the area of the conductive plates.

How does the distance between plates affect capacitance?

Capacitance is inversely proportional to the distance between the plates.

What is the permittivity of free space?

8.85 × 10^-12 F/m.

What is the formula for capacitance based on physical properties?

C = (εr ε0 A) / d.

What type of capacitor is known for high working voltage?

Mica capacitors.

What are ceramic disk capacitors known for?

Being small, nonpolarized, and having relatively high capacitance.

What is a characteristic of electrolytic capacitors?

They offer very high capacitance but are polarized and less precise.

What are variable capacitors used for?

Manual adjustment of capacitance values, often in tuning circuits.

What is a varactor diode?

A solid-state device that acts as a variable capacitor, adjusted by an electrical signal.

How are capacitor values typically marked?

Using direct reading, three-digit codes, or numbers without multipliers.

What does a three-digit code like 104 represent?

10 x 10^4 pF, which equals 0.1 μF.

What happens to total capacitance when capacitors are connected in series?

The total capacitance is less than the smallest individual capacitance.

What is the formula for total capacitance in series?

1/C_T = 1/C_1 + 1/C_2 + ... + 1/C_n.

How do you calculate total capacitance for two capacitors in series?

C_T = (C_1 * C_2) / (C_1 + C_2).

What is the capacitance of a capacitor labeled 222?

2200 pF.

What is the capacitance of a capacitor labeled 330?

330 pF.

What is the formula for total capacitance when capacitors are connected in parallel?

C_T = C_1 + C_2 + C_3 + ... + C_n

What is the total capacitance of a 1000 pF capacitor in parallel with an 800 pF capacitor?

1800 pF

What is the RC time constant?

τ = R * C, where R is resistance in ohms and C is capacitance in farads.

After one time constant (τ), what percentage of final voltage does a charging capacitor reach?

Approximately 63.2%

How long is it considered for a capacitor to be fully charged?

After about 5 time constants (5τ), it is considered fully charged (around 99.3% of final value).

What happens to the voltage across a capacitor during discharging?

It decreases exponentially.

What is the formula for instantaneous voltage across a capacitor during charging?

v = V_f + (V_i - V_f)e^(-t/RC)

What is capacitive reactance (X_C)?

The opposition a capacitor offers to alternating current (AC), which is frequency-dependent.

What is the formula for capacitive reactance?

X_C = 1 / (2πfC), where f is frequency in Hertz and C is capacitance in Farads.

What is the unit of capacitive reactance?

Ohms (Ω)

How do reactances of capacitors in series combine?

X_tot = X_1 + X_2 + X_3 + ... + X_n

How do reactances of capacitors in parallel combine?

1/X_tot = 1/X_1 + 1/X_2 + 1/X_3 + ... + 1/X_n

What is a capacitive voltage divider?

A configuration where two capacitors in series divide the input voltage based on their reactances.

What is the phase shift of current in a capacitor when AC voltage is applied?

The current leads the voltage by 90 degrees.

What is reactive power?

The rate at which energy is alternately stored and returned by a capacitor, measured in VARs (volt-amperes reactive).

What are coupling capacitors used for?

To pass AC signals between circuit stages while blocking DC components.

What is the purpose of bypass capacitors?

To provide a low-impedance path to ground for AC signals, stabilizing DC voltages or removing unwanted AC noise.

What is a dielectric?

The insulating material between the plates of a capacitor.

What is the SI unit of capacitance?

Farad (F)

What does the RC time constant (τ) represent?

The time required for the voltage or charge in an RC circuit to change by approximately 63.2% of the total difference between its initial and final values.

What is the relationship between capacitive reactance and frequency?

Capacitive reactance decreases as frequency increases.

How do you calculate the capacitive reactance of a 100 μF capacitor at a frequency of 60 Hz?

X_C = 1 / (2π(60 Hz)(0.0001 F)) ≈ 26.5 Ω.