Mastering Physics Set 4 Midterm Flashcards

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Questions and Answers

What property of objects is best measured by their capacitance?

The ability to distort an external electrostatic field

The ability to store charge (correct)

The ability to conduct electric current

How can the capacitance of an air-filled charged capacitor be increased?

Decrease the charge on the capacitor

Increase the charge on the capacitor

Increase the spacing between the plates of the capacitor

Decrease the spacing between the plates of the capacitor (correct)

How can the capacitance of a charged parallel-plate capacitor be halved?

Double the plate separation (correct)

Halve the plate area (correct)

Double the plate area

Double the charge

Which combination of changes would quadruple the capacitance of a charged parallel-plate capacitor?

Halve the plate separation and double the plate area Signup and view all the answers

If the potential of plate 1 is V, what are the potentials of plates 3 and 6?

V and 0 Signup and view all the answers

If the charge of the first capacitor is Q, what are the charges of the second and third capacitors?

2Q and 3Q Signup and view all the answers

What is the total charge Qtot for the equivalent capacitor?

Qtot = 6C Signup and view all the answers

What is the equivalent capacitance Ceq for this combination of capacitors?

Ceq = 6C Signup and view all the answers

What are the charges on plates 3 and 6?

+Q and −Q Signup and view all the answers

If the voltage across the first capacitor is ΔV1, what are the voltages across the second and third capacitors?

1/2ΔV1 and 1/3ΔV1 Signup and view all the answers

Find the voltage ΔV1 across the first capacitor.

ΔV1 = 6ΔV Signup and view all the answers

Find the charge Q on the first capacitor.

Q = CΔV1 Signup and view all the answers

Find the equivalent capacitance Ceq for this combination of capacitors in series.

Ceq = 6C/11 Signup and view all the answers

Which statements are correct regarding the arrangement of capacitors?

C3 is in parallel with C1 and C2 Signup and view all the answers

What is the equivalent capacitance Ceq of the entire combination?

Ceq = 14.4 μF Signup and view all the answers

How would you expect the equivalent capacitance Ceq to compare to the values of each individual capacitor?

Ceq must be less than C4 Signup and view all the answers

What is the voltage across capacitor 2 if capacitor 1 has voltage V and area of capacitor 2 is double?

2V Signup and view all the answers

What spacing should capacitor 2 have to make the capacitance of both capacitors equal?

2d Signup and view all the answers

Find the equivalent capacitance CA of the network of capacitors.

CA = 2.59 μF Signup and view all the answers

Find the equivalent capacitance CB of the new network of capacitors.

CB = 2.54 μF Signup and view all the answers

Find the energy dissipated in the resistor.

Ur = U/K Signup and view all the answers

What is Ur in the case where the charging battery remains connected while the dielectric is inserted?

Ur = KU Signup and view all the answers

What is the magnitude of the potential difference ΔV between two concentric spherical shells?

ΔV = 38.7 V Signup and view all the answers

What is the electric-field energy stored in the spherical capacitor?

6.38×10^−8 J Signup and view all the answers

Find the energy U0 stored in an air-filled parallel-plate capacitor.

U0 = 1/2(ϵ0A/d)V^2 Signup and view all the answers

What is the new energy U1 of the capacitor after its plates are pulled apart?

U1 = 3ϵ0(AV^2)/2d Signup and view all the answers

Find the energy U2 of the dielectric-filled capacitor.

U2 = 1/2(V^2)(Kϵ0A/d) Signup and view all the answers

Rank the following capacitors on the basis of the dielectric constant of the material between the plates:

A=2cm^2 C=8nF = Higher Dielectric Constant A=2cm^2 C=4nF = Lower Dielectric Constant A=1cm^2 C=1nF = Lowest Dielectric Constant A=4cm^2 C=2nF = Intermediate Dielectric Constant A=4cm^2 C=1nF = Lower Dielectric Constant A=8cm^2 C=2nF = Higher Dielectric Constant Signup and view all the answers

Rank the capacitors on the basis of the charge stored on the positive plate:

A=2cm^2 C=8nF = Highest Charge A=2cm^2 C=4nF = Intermediate Charge A=4cm^2 C=2nF = Lower Charge A=8cm^2 C=2nF = Lowest Charge A=1cm^2 C=1nF = Lowest Charge A=4cm^2 C=1nF = Lower Charge Signup and view all the answers

Study Notes

Capacitance and Charge Storage

Capacitance quantifies an object's ability to store electric charge.
Increasing capacitance can involve decreasing the distance between capacitor plates or increasing plate area.

Modifying Capacitance

Doubling plate area increases capacitance; halving plate area decreases it.
Halving plate separation and doubling plate area results in quadrupling capacitance.

Charge Distribution and Potential

In a system of capacitors, charges are distributed based on individual capacitances; if one has charge Q, others might have 2Q and 3Q.
Potential difference across capacitors can be expressed in ratios depending on configurations, such as ΔV1 being twice or half of other voltages.

Equivalent Capacitance

Total charge Qtot for a system can be expressed in terms of voltage and individual capacitances.
The equivalent capacitance (Ceq) can be calculated based on the arrangement of capacitors—series and parallel connections yield different values.

Capacitor Connection Scenarios

Capacitors can be in distinct configurations: capacitors C3 and C1/C2 may be arranged in parallel while C1 and C2 are in series.
The equivalent capacitance is expected to be less than the individual capacitances of connected capacitors.

Voltage and Distance Relations

For capacitors with the same charge but differing areas, the voltage across larger area capacitors will be lower (V/2 in one scenario) if plate separation is consistent.
Adjusting plate spacing is essential for equal capacitance between different capacitor configurations.

Energy in Capacitors

The energy stored (U0) in a capacitor depends on area, plate separation, and voltage, defined by the formula U0 = 1/2(ϵ0A/d)V^2.
Energy changes when capacitors are disconnected from batteries and later interact with dielectrics, with formulations changing according to various physical constants.

Special Cases of Capacitors

A spherical capacitor with specified radius and charge calculates potential difference (ΔV = 38.7 V) and electric-field energy (6.38×10^−8 J).
Final expressions of energy in systems involving dielectrics and changing plate separations simplify calculations drastically, illustrating relationships among voltage, dielectric constants, and area.

Capacitance and Dielectric Constants

Capacitors are often analyzed by their dielectric constants, affecting overall capacitance and charge storage capabilities.
Ranking capacitors by dielectric constants and charge stored helps in understanding their performance in electric systems.

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Test your knowledge of capacitance and capacitor properties with these flashcards. This set covers key concepts needed for understanding basic physics principles. Enhance your preparation for the midterm exam effectively.