Capacitance

When we attach a battery to a capacitor, the capacitor charges up. The capacitor stops charging when...

the potential difference between the capacitor plates = the potential difference across the batter

What are dielectrics and what happens to an electric field through a dielectric?

• A dielectric is an insulating material that can polarise in the presence of an electric field.

• The polarized molecules in the dielectric generate their own internal electric field that opposes the direction of the external electric field.

• This opposing field partially cancels out the external field, resulting in a weaker net electric field within the dielectric than would be present if no dielectric were there.

• Due to the reduced electric field, a dielectric material increases the capacitor’s ability to store charge due to decreased voltage(V=Ed), effectively increasing its capacitance.

What is permittivity and its relationship with strength of electric field?

• Permittivity is a measure of a material’s ability to permit electric field lines through it.

• Higher permittivity in a dielectric increases capacitance by reducing the resultant electric field due to polarization, which allows more charge to be stored for the same voltage.

• The weaker resultant field is due to the dielectric’s internal polarization, which creates an opposing field that partially cancels the field generated by the capacitor plates.

• A higher ε_r means a greater ability to reduce the field, leading to a higher capacitance.

Relationship between area of each plate on capacitance

• Direct Proportionality: The capacitance C is directly proportional to the area A of each plate. This means that increasing the area of the plates increases the capacitance, and decreasing the area of the plates decreases the capacitance.

• Why This Happens: A larger plate area allows for more electric field lines to exist between the plates, which enables the capacitor to store more charge at the same voltage. Essentially, a larger area provides more "space" for charge to accumulate.

Effect of distance on capacitance

Since E remains constant (for a given Q), increasing d directly increases V. According to the definition of capacitance:

Q=CV

an increase in V (for the same Q) results in a decrease in capacitance. In other words, increasing the plate distance d increases the voltage required to store the same amount of charge, thus lowering the capacitance.

How is energy stored in a capacitor?

As a capacitor charges a pd is introduced across the plates which means work is done to move electrons away from the positive plate to the negative plate and store energy in the electric field.

The energy (E) stored in a capacitor can be expressed as E= 1/2 CV², where C is capacitance and V is the voltage across the plates.

The electrical potential energy stored is the work done to move the extra charge onto the plates against the potential difference across the plates.

what is the time constant for a charging capacitor vs a discharging capacitor

• The time taken for the charge of a charging capacitor to rise to about 63% of Peak charge (Q₀)

• The time taken for the charge on a discharging capacitor to fall to about 37% of Q₀

Explain why a capacitor would not be a good source for powering a portable media player

• Since capacitors can only store a relatively small amount of charge, it would have to be very large to provide enough power, which might hinder the portability of the media player

• It could only power the device for a short time, so it would need charging very often

• The voltage would decrease as capacitor discharged , so it would be difficult to produce a constant output

Definition of capacitance

The amount of charge the capacitor can store per unit potential difference across it

Explain how you could keep the current charging a capacitor constant

Use a variable resistor - constantly alter the resistance in the circuit to keep the current the same.

Why is the energy stores in the capacitor ½ QV?

The energy stored by the capacitor is half the energy supplied by the power source, the rest is lost to the resistant in the circuit and the internal resistance of the battery

Explain why a build-up of charge in a capacitor results in a build-up of energy, and state what type of energy is stored in a capacitor.

Like charges are forced together, against their electrostatic repulsion, onto the plates. Some of the energy taken to force them together is stored as electrical potential energy.

How do capacitors work/ charging process?

1. Switch closed creating an electric field in the capacitor(positive to negative as this is the conventional current which is the direction of the field)

2. Electric field attracts electrons on the negative plate (real current is the movement of electrons from negative terminal to positive terminal so electrons from the negative terminal are attracted to the negative plate) - Negative charge builds up on that plate

3. At the same time, electrons flow from the other plate to the positive terminal of the supply, making that plate positive. These electrons are repelled by the negative charge on the negative plate and attracted to the positive terminal of the supply.

4. When capacitor is fully charged there are so many electrons piled that they repel any other electrons coming towards it. Electrostatic repulsion makes it harder and harder for electrons to be deposited.

5. When p.d across the supply = pd across the capacitor, the current falls to 0

6. Capacitor is fully charged

As soon as the switch is closed and current starts to flow explain what happens with potential difference as capacitor charges.

The potential difference is 0 at first, so there is no p.d opposing the current.

The p.d of the battery causes an initial relatively high current to flow.

As the capacitor charges, the p.d across the capacitor gets bigger, the p.d across the resistor gets smaller, and current drops.

This explains the graph shapes

Explain discharging through a fixed resistor, how it is done and what happens when capacitor is fully discharged

To discharge a capacitor, take out battery and reconnect circuit

When a charged capacitor is connected across a resistor, the p.d drives a current though a circuit.

This current flows in the opposite direction from the charging current,

The capacitor is fully discharged when the p.d across the plates and the current in the circuit are both 0

The amount of charge left on the plates falls exponentially with time

What are polar molecules and their relationship with electric fields and reference permittivity and hence effect on capacitance?

Polar moelecules have a positive end and a negative end. When no charge is being stored by a capacitor , no electric field is being generates so the molecules are aligned randomly

When there is a charge, the positive ends of the molecules are attracted to the negative plate and vice versa. Hence causes molecules to align themselves anti-parallel to the electric field.

The molecules have their own electric field, which in this alignment now opposes the applied electric field.

The larger the permittivity, the larger this opposing field is.

This reduces the overall electric field between the parallel plates, which reduces the p.d needed to transfer a given charge to the capacitor, Hence capacitance increases(Q=CV)

Explain why there is an increase in the energy stored by the capacitor when the polythene sheet is pulled out from between the plates.

• In the polar dielectric molecules align in the field with positive charged end towards the negative plate.

• Hence when this dielectric is removed work is done on the capacitor separating the positively charged surface of the dielectric from the negatively charged plate

When capacitor is fully charged what is happening in a circuit with cell, capacitor and fixed resistor?

Refer to how the potential difference across the resistor and the capacitor change with time, the energy changes which take place in circuit

when the capacitor is fully charged:

• V_r decreases from E to zero whilst V_c increases from zero to E

• at any time V_r + V_c = E

• time variations are exponential decrease for V_r and exponential increase for V_c

• chemical energy of the battery is changed into electric potential energy stored in the capacitor, and into thermal energy by the resistor (which passes to the surroundings)

• half of the energy supplied by the battery is converted into thermal energy and half is stored in the capacitor

When capacitor is fully discharged what is happening in circuit of cell, fixed resistor and capacitor?

Refer to how the potential difference across the resistor and the capacitor change with time, the energy changes which take place in circuit

when the capacitor is fully discharged:

• V_c decreases from –E to zero and V_r decreases from E to zero

• at any time V_c = – V_r

• both V_c and V_r decrease exponentially with time

• electrical energy stored by the capacitor is all converted to thermal energy by the resistor as the electrons flow through it and this energy passes to the surroundings

• time constant of the circuit is the same for discharging as for charging

Explain why the rate of change of pd between the capacitor plates decreases as the capacitor discharges

current decreases and charge lost more slowly so pd falls more slowly because V is proportional to Q

Mica a dielectric is made up of polar molecules.

As the mica is inserted, the capacitance of the capacitor changes

Explain how the polar molecules cause this change in capacitance.

• Electric field exists between the plates

• Polar molecules align with their positive side facing the negative plate.

• This produced a counter field, reducing the existing field between the plates

• Since Ed = V as E decreases the pd, V reduces between the capacitor plates

• Charge, Q remains the same so capacitance increases.

State and explain a change to one control setting on the oscilloscope that would reduce the uncertainty in the value of the time constant.

• Reduce the time base setting

• Uncertainty is due to the smallness of divisions and this action means the trace is stretched horizontally

• Another is increase the y gain

• Uncertainty is due to the smallness of divisions and this action means the trace is stretched vertically

Explain the use of the mirror when reading an analogue voltmeter

Move position until needle is aligned with its reflection in the mirror

This ensures scale is read from directly above.