Capacitance Concepts in Physics

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Questions and Answers

How does increasing the area of the conducting plates affect capacitance?

  • Capacitance decreases
  • Capacitance fluctuates unpredictably
  • Capacitance remains the same
  • Capacitance increases (correct)

What effect does decreasing the distance between conducting plates have on capacitance?

  • Capacitance becomes negligible
  • Capacitance decreases
  • Capacitance increases (correct)
  • Capacitance becomes infinite

Which type of dielectric material would result in higher capacitance?

  • An insulator with no conductivity
  • A less conductive material (correct)
  • A material with higher resistivity
  • A material that is a good conductor

If the charge is $0.3 imes 10^{-6} C$ and the voltage is $1 imes 10^{3} V$, what is the capacitance?

<p>0.0003 F (A)</p> Signup and view all the answers

Which of the following describes a parallel-plate capacitor?

<p>Contains two parallel plates separated by a dielectric (B)</p> Signup and view all the answers

What is the impact of using a more conductive dielectric on capacitance?

<p>Decreases capacitance (C)</p> Signup and view all the answers

Which shape of capacitor is typically associated with specific advantages in capacitance?

<p>Cylindrical capacitors (B)</p> Signup and view all the answers

What is the role of the insulator in a capacitor?

<p>Helps in maintaining charge storage (C)</p> Signup and view all the answers

What is the value of the electric field $E$ created by a charge $Q$ of $15 , \mu C$ at a distance of $0.20 \text{ m}$?

<p>36,734 N/C (D)</p> Signup and view all the answers

When a test charge of $q = 0.80 , \mu C$ is placed in the electric field of $Q$, what is the value of the force $F_e$ acting on it?

<p>7.35 x 10^-16 N (A)</p> Signup and view all the answers

What is the correct formula for calculating the electric field $E$ due to a point charge?

<p>$E = \frac{k q}{r^2}$ (C)</p> Signup and view all the answers

If the distance $r$ between the source charge and the test charge is halved, what effect does this have on the electric field $E$?

<p>It quadruples $E$ (C)</p> Signup and view all the answers

What dimensionless constant is used in calculating the electric field of a point charge?

<p>k (A)</p> Signup and view all the answers

What is the result of substituting the given values into the formula $E = \frac{k |Q|}{r^2}$ with $Q = 15 \mu C$ and $r = 0.20 m$?

<p>36,734 N/C (C)</p> Signup and view all the answers

For the test charge $q$ of $0.80 , \mu C$, what is the relationship between the force $F_e$ and the electric field $E$?

<p>$F_e = E q$ (C)</p> Signup and view all the answers

When calculating the force between two charges, which of the following factors does NOT affect the force $F_e$?

<p>The direction of the electric field (C)</p> Signup and view all the answers

What is the value of the total capacitance (CT) for capacitors C1 and C2 connected in parallel?

<p>8.2 x 10^-12 F (C)</p> Signup and view all the answers

What is the formula used to calculate charge (Q) on a capacitor?

<p>Q = C * V (D)</p> Signup and view all the answers

If the voltage (VT) across the capacitors is 1600 V, what is the charge (Q1) on capacitor C1, given that C1 = 3.5 x 10^-12 F?

<p>5.6 x 10^-12 C (A)</p> Signup and view all the answers

What is the relationship between the voltages across capacitors in parallel?

<p>V1 = V2 = VT (A)</p> Signup and view all the answers

What is the equivalent capacitance when capacitors C1 = 4 μF, C2 = 2 μF, and C3 = 3 μF are connected in series?

<p>0.714 μF (D)</p> Signup and view all the answers

In the calculated circuit with C1, C2, and C3 in series, what would be the total charge (QT) if the voltage across them is 12 V?

<p>0.00084 C (B)</p> Signup and view all the answers

Which of the following statements about capacitors in parallel is true?

<p>The total charge is the sum of charges on individual capacitors. (A)</p> Signup and view all the answers

What is the total voltage (VT) across capacitors C1 and C2 if both are connected in parallel and VT = 1600 V?

<p>1600 V (B)</p> Signup and view all the answers

What is the electric flux $ abla E$ in the scenario depicted?

<p>$8.17 \times 10^{20} V - m$ (D)</p> Signup and view all the answers

From the given information, what value of $ heta$ was used in the calculation of the electric flux $ abla E$?

<p>$75^ ext{o}$ (D)</p> Signup and view all the answers

What is the relationship described by Gauss's Law?

<p>The electric flux through a closed surface equals the net charge inside divided by permittivity. (D)</p> Signup and view all the answers

What is the formula to calculate work done in bringing two charges closer together?

<p>$k \frac{Q_1 Q_2}{r}$ (D)</p> Signup and view all the answers

What is the electric field strength used in the second example?

<p>$9.5 \times 10^{13} N/C$ (D)</p> Signup and view all the answers

In the context of electric fields, what can be said about regularly shaped bodies?

<p>Electric fields can be predicted analytically due to uniform charge distribution. (C)</p> Signup and view all the answers

What is the unit of electric flux as mentioned in the content?

<p>Newton meters squared per Coulomb (Nm²/C) (B)</p> Signup and view all the answers

What is the value of the electric flux $ abla E$ calculated in the first example?

<p>$8.17 \times 10^{20} V - m$ (D)</p> Signup and view all the answers

What is the formula for calculating charge (Q) in terms of capacitance (C) and voltage (V)?

<p>Q = CV (C)</p> Signup and view all the answers

If C2 is 4.7 x 10^-12 F and V2 is 1600 V, what is the charge Q2?

<p>7.52 x 10^-9 C (C)</p> Signup and view all the answers

What is the total capacitance (C34) of two capacitors connected in series, C3 and C4?

<p>7.5 x 10^-7 F (D)</p> Signup and view all the answers

Given capacitance values C1 = 4 x 10^-6 F and C2 = 2 x 10^-6 F, what is the formula to obtain C12 for these capacitors in parallel?

<p>C12 = C1 + C2 (C)</p> Signup and view all the answers

If the voltage across capacitor C4 is given as 9 V, what can be inferred about C4?

<p>Its charge can be calculated. (D)</p> Signup and view all the answers

Which relationship is true for the configuration of capacitors C1 and C2?

<p>C12 = C1 + C2 (B)</p> Signup and view all the answers

Which of the following describes the formula for finding the total capacitance C12 of two capacitors connected in series?

<p>C12 = 1/(1/C1 + 1/C2) (A)</p> Signup and view all the answers

Given a capacitance value of C34 = 7.5 x 10^-7 F, what does this imply about C3 and C4?

<p>They can be treated as a single capacitor of 7.5 x 10^-7 F. (C)</p> Signup and view all the answers

What is the electric potential $V_E$ for the given charge $Q = +5.02 \times 10^{-13} C$ at a distance of $r = 2.08 \times 10^{-3} m$?

<p>2.17 V (B)</p> Signup and view all the answers

At what distance would the electric potential be $7.94 \times 10^6 V$ for a point charge of $Q = +4.02 \times 10^{-15} C$?

<p>$4.55 \times 10^{-12} m$ (B)</p> Signup and view all the answers

Which statement accurately describes equipotential lines?

<p>They are perpendicular to the electric field lines. (B)</p> Signup and view all the answers

What is the value of the electric field $E$ created by the charge $Q = +5.02 \times 10^{-13} C$ at a distance of $2.08 \times 10^{-3} m$?

<p>$1.04 \times 10^{5} \text{ N/C}$ (A)</p> Signup and view all the answers

For a dipole, what is true about the equipotential surfaces around it?

<p>They are everywhere perpendicular to the electric field lines. (B)</p> Signup and view all the answers

What type of charge creates circular equipotential lines?

<p>Positive point charge (D)</p> Signup and view all the answers

Which equation describes the relationship between electric potential $V_E$, charge $Q$, and distance $r$?

<p>$V_E = \frac{kQ}{r}$ (C)</p> Signup and view all the answers

What characteristic describes the electric field lines around a uniformly charged plane?

<p>They are uniformly spaced and parallel. (B)</p> Signup and view all the answers

Flashcards

Coulomb's Law

The electric force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Electric Field Strength

The electric field strength at a point is the force per unit positive charge that would be experienced by a test charge placed at that point.

Electric Force

The electric force on a charge is equal to the product of the charge and the electric field strength at the point where the charge is located.

Electric Potential

A scalar quantity that represents the potential energy per unit charge at a point in an electric field.

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Electric Potential Difference

The work done per unit charge in moving a charge from one point to another in an electric field.

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Capacitance

A measure of the ability of a material to store electric charge.

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Electrostatic Induction

The process of charging an object without direct contact by bringing a charged object close to it.

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Electric Current

The flow of electric charge through a conductor.

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Capacitor

A device that stores electrical energy in an electric field.

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Dielectric

The insulating material between the plates of a capacitor.

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Area of Conducting Plates

The area of the conducting plates affects the capacitance. A larger area means more space to store charge.

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Distance Between Plates

The distance between the conducting plates affects the capacitance. A smaller distance means a stronger electric field and greater capacitance.

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Type of Dielectric

The type of dielectric used in a capacitor affects its capacitance. A more conductive dielectric increases capacitance.

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Parallel-Plate Capacitor

A capacitor with two parallel plates separated by a dielectric material.

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Charge and Voltage Relationship

The amount of charge stored in a capacitor is directly proportional to the applied voltage. More voltage, more charge.

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Capacitors in Series

Total capacitance in a series circuit is the inverse of the sum of the inverses of individual capacitances. This means every capacitance is considered separately, and the combined effect is lower than the smallest individual capacitance.

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Capacitors in Parallel

Total capacitance in a parallel circuit is the sum of all individual capacitances. This means each capacitance contributes directly to the total, resulting in a higher overall capacitance.

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Charge Storage in a Capacitor

The charge stored on a capacitor is directly proportional to the voltage applied across it. This means if you double the voltage, you double the charge stored.

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Voltage Across a Capacitor

The voltage across a capacitor is directly proportional to the charge stored on it. This means if you increase the charge, the voltage across the capacitor also increases.

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Equivalent Capacitance

The equivalent capacitance of a circuit represents the overall capacitance of the circuit, acting as a single capacitance that would store the same amount of charge at the same voltage as the original circuit.

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Total Charge in a Circuit

The total charge stored in a circuit is equal to the sum of the charges stored on each individual capacitor.

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Voltage Distribution in Series

The total voltage across a series circuit is the sum of the voltages across each individual capacitor. This means the voltage divides among the capacitors in a series circuit.

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Voltage in Parallel Circuit

The voltage across each capacitor in a parallel circuit is the same. This means all capacitors experience the same voltage in a parallel circuit.

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Charge stored in a capacitor (Q)

The amount of electric charge stored in a capacitor.

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Voltage across a capacitor (V)

The potential difference across the capacitor's plates.

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Capacitance Formula

The relationship between capacitance, charge, and voltage. It states that the charge stored in a capacitor is directly proportional to the capacitance and the voltage across the capacitor.

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Gauss's Law

The total electric flux through any closed surface is proportional to the net electric charge enclosed by the surface.

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Electric Flux

The electric flux through a surface is a measure of the number of electric field lines passing through that surface.

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Electric Flux for closed surfaces

The electric flux through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space.

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Electric Field

The electric field is a region where a charged object experiences a force.

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Work done bringing charges closer

The work done in bringing two charges closer together from infinity to where they are separated by the distance r.

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Work (Joules)

Work is measured in Joules (J) and is a scalar quantity.

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Equipotential Lines

Equipotential lines are imaginary surfaces where the electric potential is constant. Every point on an equipotential line has the same electric potential energy.

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Electric Potential of a Point Charge

The electric potential due to a point charge is directly proportional to the magnitude of the charge and inversely proportional to the distance from the charge.

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Equipotential Lines and Electric Field Lines

Equipotential lines are always perpendicular to electric field lines. This indicates that no work is done when moving a charge along an equipotential line.

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Electric Potential Energy

Electric potential energy is the potential energy that a charge possesses due to its position in an electric field.

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Electric Potential and Charge and Distance

The electric potential at a point is directly proportional to the charge creating the electric field and inversely proportional to the distance from the charge.

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Equipotential Lines for a Dipole

Equipotential lines for a dipole are symmetrical about the center point of the dipole. They form continuous loops around the charges.

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Study Notes

Electrostatics

  • Electrostatics is the study of stationary electric charges and the forces between them
  • Electric charge is a fundamental property of matter.
  • Charges of the same sign repel, charges of opposite sign attract
  • Charge is conserved, meaning it cannot be created or destroyed.
  • Charge is quantized, meaning it exists in discrete units. The elementary charge (e) is the smallest unit of charge (1.602 x 10⁻¹⁹ C).
  • Coulomb's law describes the force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them

Electric Charge

  • Subatomic particles possess electric charge (e.g., protons (+), electrons (-), and neutrons (0))
  • The elementary charge (e) is the smallest unit of electric charge, equal to 1.602 × 10⁻¹⁹ coulombs
  • Charge is quantized, meaning it exists in integer multiples of the elementary charge

Coulomb's Law

  • Coulomb's Law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them
  • Mathematically, this is expressed as F = k|qq₂|/r². Where:
    • F is the force between the charges
    • k is Coulomb's constant (approximately 8.99 x 10⁹ N⋅m²/C²)
    • q₁ and q₂ are the magnitudes of the two charges
    • r is the distance between the charges

Charging by Friction

  • Rubbing two different materials together can transfer electrons from one material to the other
  • This process results in static charges on each material.

Charging by Induction

  • An electrically charged object can induce a charge in a neutral object without direct contact
  • The charged object generates an electrical field that rearranges the charges in the neutral object, creating a separation of positive and negative charges. This can happen in conductors

Charging by Conduction

  • When a charged object touches a neutral object, electrons flow between the objects, equalizing the charge.

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