6.1 - Capacitors

What is a capacitor?

• A capacitor is an electrical component that stores charge on 2 separate metallic plates

• An insulator, called a dielectric, is placed between the plates to prevent the charge from traveling across the gap

What is capacitance?

The capacitance, C, is the charge stored, Q, per unit potential difference, V, across the 2 plates.

Therefore, we have C = Q / V.

It is measured in Farads, F (1F = 1CV⁻¹)

What is the relative permittivity (a.k.a dielectric constant)?

• The ratio of the charge stored with the dielectric between the plates to the charge stored when dielectric is not present.

• εᵣ = Q / Q₀

• The greater the relative permittivity, the greater the capacitance of the capacitor

What is the equation for the total capacitance in series?

1 / C total = 1 / C1 + 1 / C2 +……

What is the equation for the total capacitance in parallel?

Total = C1 + C2 + …

What does the area under the graph of charge against pd represent?

The energy stored by the capacitor.

Describe the Q against t graph for the DISCHARGING of a capacitor through a resistor.

Charge decreases rapidly, then slowly levels out over time.

Reverse exponential.

Describe the V against t graph for the DISCHARGING of a capacitor through a resistor.

V decreases rapidly at first, then levels out over time.

Reverse exponential.

Describe the I against t graph for the DISCHARGING of a capacitor through a resistor.

I decreases rapidly at first, then levels out over time.

Reverse exponential.

Describe the Q against t graph for the CHARGING of a capacitor through a resistor.

charge increases rapidly at first, slowly leveling out with time. (still increasing though)

Describe the V against t graph for the CHARGING of a capacitor through a resistor.

Voltage increases rapidly at first, then slowly levels out with time (still increasing though)

What is the time constant?

The time it takes for the charge in a capacitor to fall to 37% (e⁻¹) of the initial value given by resistance x capacitance.

Considered full discharged after 5 time constants.

How does a capacitor charge up?

1) Electrons move from negative to positive around circuit

2) Electrons deposited on plate A, making it negative

3) Electrons travel from plate B to positive terminal giving plate positive charge.

4) Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating PD across plates

5) When PD across plates = PD source, fully charged

Describe and explain in terms of the movement of electrons how the PD across a capacitor changes, when it discharges across a resistor.

• Electrons move in opposite direction than when capacitor was charging

• Charge on one plate A decreases as it loses electrons, plate B gains electrons, neutralizing them

• PD decreases exponentially across the plates

what 2 factors affect time taken for capacitor to charge/discharge?

• Capacitance

• Resistance of circuit

How to find the value of 𝓔?

𝓔 = 𝓔r x 𝓔0

(𝓔r is our relative permittivity)

(𝓔0 is permittivity of free space)