Lesson test: Capacitance and dielectrics

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Capacitance and dielectrics

1.[3p]
Two parallel plates of area 100 cm² are separated by 0.20 mm of mica, of dielectric constant 5.4. What is the capacitance, in nanofarads?

CorrectNot quite: 2.39

2.[3p]
Every capacitor in a series chain carries the same charge because

the conductor between two of them is isolated, so the charge drawn to one side must leave an equal charge on the other

Correct

charge always divides equally between components

The answer is: the conductor between two of them is isolated, so the charge drawn to one side must leave an equal charge on the other

the voltage across each is the same

The answer is: the conductor between two of them is isolated, so the charge drawn to one side must leave an equal charge on the other

series capacitors are identical by definition

The answer is: the conductor between two of them is isolated, so the charge drawn to one side must leave an equal charge on the other

3.[2p]
Capacitors of 2.0 μF, 6.0 μF and 3.0 μF are connected in series. What is the total capacitance, in microfarads?

CorrectNot quite: 1.0

4.[2p]
A 50 μF capacitor is charged to 400 V. How much energy does it store, in joules?

CorrectNot quite: 4.0

5.[2p]
Where does the factor of one half in $U = \frac{1}{2} Q V$ come from?

The voltage rises from zero to $V$ during charging, so the average charge crosses half of $V$

Correct

Half the charge is lost to the surroundings

The answer is: The voltage rises from zero to $V$ during charging, so the average charge crosses half of $V$

It is the fraction of the field that lies between the plates

The answer is: The voltage rises from zero to $V$ during charging, so the average charge crosses half of $V$

It comes from the two plates each holding half the energy

The answer is: The voltage rises from zero to $V$ during charging, so the average charge crosses half of $V$

6.[2p]
An air capacitor at the breakdown field of air stores about nine orders of magnitude less energy per cubic metre than petrol does.

True

Correct

False

The answer is: True

7.[3p]
Inserting a dielectric at fixed charge lowers the field between the plates because

the polarised molecules leave a bound surface charge that partly cancels the free charge on each plate

Correct

the dielectric conducts some of the charge away

The answer is: the polarised molecules leave a bound surface charge that partly cancels the free charge on each plate

the plates move closer together

The answer is: the polarised molecules leave a bound surface charge that partly cancels the free charge on each plate

the dielectric absorbs the field as heat

The answer is: the polarised molecules leave a bound surface charge that partly cancels the free charge on each plate

8.[3p]
Which of these are true of a material with a very high dielectric constant but a poor breakdown field?

Select all that apply

It may store less energy than a lower- $κ$ material, since the usable field is capped

Correct

Energy density goes as $κ E^{2}$ , so the two properties trade against each other

Correct

It is always the better choice, since capacitance is proportional to $κ$

The answer is: It may store less energy than a lower-$\kappa$ material, since the usable field is capped, Energy density goes as $\kappa E^2$, so the two properties trade against each other

Its dielectric constant is guaranteed to hold up at high frequency

The answer is: It may store less energy than a lower-$\kappa$ material, since the usable field is capped, Energy density goes as $\kappa E^2$, so the two properties trade against each other

9.[2p]
Match each capacitor relation to the arrangement it describes.

Capacitances add
Reciprocals of capacitance add
Charge is the same in each
Voltage is the same across each

a parallel pair
a series chain
two capacitors in series
two capacitors in parallel

Show the answer

Capacitances add: two capacitors in parallel Reciprocals of capacitance add: two capacitors in series Charge is the same in each: a series chain Voltage is the same across each: a parallel pair

1.[3p] Two parallel plates of area 100 cm² are separated by 0.20 mm of mica, of dielectric constant 5.4. What is the capacitance, in nanofarads?

2.[3p] Every capacitor in a series chain carries the same charge because

3.[2p] Capacitors of 2.0 μF, 6.0 μF and 3.0 μF are connected in series. What is the total capacitance, in microfarads?

4.[2p] A 50 μF capacitor is charged to 400 V. How much energy does it store, in joules?

5.[2p] Where does the factor of one half in U=12QV come from?

6.[2p] An air capacitor at the breakdown field of air stores about nine orders of magnitude less energy per cubic metre than petrol does.

7.[3p] Inserting a dielectric at fixed charge lowers the field between the plates because

8.[3p] Which of these are true of a material with a very high dielectric constant but a poor breakdown field?

9.[2p] Match each capacitor relation to the arrangement it describes.

1.[3p]
Two parallel plates of area 100 cm² are separated by 0.20 mm of mica, of dielectric constant 5.4. What is the capacitance, in nanofarads?

2.[3p]
Every capacitor in a series chain carries the same charge because

3.[2p]
Capacitors of 2.0 μF, 6.0 μF and 3.0 μF are connected in series. What is the total capacitance, in microfarads?

4.[2p]
A 50 μF capacitor is charged to 400 V. How much energy does it store, in joules?

5.[2p]
Where does the factor of one half in $U = \frac{1}{2} Q V$ come from?

6.[2p]
An air capacitor at the breakdown field of air stores about nine orders of magnitude less energy per cubic metre than petrol does.

7.[3p]
Inserting a dielectric at fixed charge lowers the field between the plates because

8.[3p]
Which of these are true of a material with a very high dielectric constant but a poor breakdown field?

9.[2p]
Match each capacitor relation to the arrangement it describes.