Physics 6.1

Capacitors

What is a capacitor?

An electrical component that stores charge

What does a capacitor look like?

2 separated metallic plates which store charge, with an insulator placed between them to prevent charge travelling across the gap

What is capacitance? (C)

Charge stored per unit pd across the 2 plates

What equation links capacitance, charge, and pd?

C=Q/V

What is capacitance measured in?

Farads (f)

What is the relative permittivity?

Ratio of charge stored with the dielectric between plates to charge stored without dielectric present

What happens to pd across a capacitor as it is charged?

• Initial pd is 0

• Increases with time

What happens to pd across a resistor as a capacitor is charged?

• Initial pd = pd of cell

• Decreases with time

What happens to charge when a capacitor is connected to a dc power supply?

• Power supply draws electrons from 1 plate and deposits them on the other

• First plate has charge +Q second has charge -Q

• These charges are equal and opposite

What happens to current as a capacitor charges?

• Decreases at the same rate as the pd across the resister

• Eventually reaches 0

What is a dielectric?

An insulator

How does the dielectric affect the capacitance of the device?

Increases the capacitance: polarises in the electric field, increases charge stored on the plates

How is a capacitor charged?

• Elections flow from negative terminal of cell to negative plate

• Excess electrons on negative plate repel electrons off positive plate which move towards positive terminal of cell

• Plates acquire an equal and opposite charge

What is kirchoff's voltage law?

The sum of the EMFs in any closed loop is equal to the sum of the potential differences in that loop

How can we find the total capacitance in series?

1/CT = 1/C1 + 1/C2 + 1/C3

What is the total charge in series?

QT=Q1=Q2

What is kirchhoff's current law?

Total current flowing into a node = total current flowing out of node

How can we find the total capacitance in parallel?

CT = C1 + C2 + C3

What is the total charge in parallel?

QT = Q1+Q2

When is work done in a capacitor?

• To push electrons to the negative plate

• To pull electrons away from positive plate

What is voltage?

Electrical potential energy per unit charge

What does the area under a voltage-charge graph represent?

Work done in charging up the capacitor - the energy stored in the capacitor

What are the energy equations for capacitors?

• W = ½QV

• W = ½CV

• W =Q²/2C

Why are capacitors useful?

They can store and discharge large quantities of energy in a short time

What are some applications of capacitors?

• Short pulses of energy: camera flashes, touch screens

• UPSs (backup power supplies): in data centres to protect hardware, hospitals in life support machines

• To convert AC to DC: in a smoothing circuit a capacitor stores energy as pd rises and discharges as it falls

How can a capacitor be discharged?

• Disconnect the power supply

• Connect a resister across capacitor

• Excess electrons flow from negative plate to positive plate, decreasing charge

What is the time constant?

• A measure of how long exponential decay will take in a circuit

• Time taken for pd, current, or charge to fall to 0.37 of its original amount

What is time constant equal to?

t= CR

What are the discharging equations for pd, current, and charge?

• V = V0e^(-t/CR)

• Replace V with I or Q

Describe the discharging graphs of V, I, and Q against time

Exponential decreasing curve

How can a graph of lnV against t be compared to y=mx+c?

• lnV/t = lnV0 - 1/ť

• 1/ť = m

• lnV0 = c

Describe iterative modelling in capacitors?

• (Change in Q)/( change in t) = - Q/CR

• Start with known Q0 and ť

• Pick t much smaller than ť

• Calculate charge leaving capacitor: (change in Q) = (change in t)xQ / CR

• Charge left: subtract change in Q

What is the charging equation for pd or charge of capacitor?

Vc = V0(1-e^(-t/CR))

Describe the charging graph of pd and charge against time

Increasing, exponential decrease