Physics: Circuits and Resistance Concepts

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Questions and Answers

If the length of a wire is doubled and its cross-sectional area is halved, how will the resistance of the wire change?

  • The resistance will double.
  • The resistance will quadruple. (correct)
  • The resistance will increase by a factor of 4.
  • The resistance will remain the same.

Two charges, q1=+2 C and q2=−3 C are placed 4 m apart. What is the correct approach to calculate the electric field at a point midway between them?

  • Use Coulomb’s law to find the field vectors due to each charge and add them using vector addition. (correct)
  • Ignore the charges since the point is equidistant from both.
  • Use Coulomb’s law to calculate the field due to each charge and then add the magnitudes of the fields directly.
  • Find the net charge and use Coulomb’s law to calculate the total field.

Which principle calculates the net electric field at a point due to multiple charges?

  • Gauss's law applied to point charges
  • The superposition principle, summing vector contributions from each charge (correct)
  • Coulomb's law and the principle of charge conservation
  • Subtracting the weaker charge field from the stronger one

According to the formula R=ρ L/A​, which of the following statements is correct regarding the relationship between resistance, length, and cross-sectional area of a wire?

<p>The resistance of a wire decreases as its cross-sectional area increases. (B)</p> Signup and view all the answers

A charge of an atom, q=+4 C is placed 6 m apart along a straight line. What is the magnitude of the net electric field?

<p>9.0 x 108 N/C (A)</p> Signup and view all the answers

A light bulb has a resistance of 12 Ω. When connected to a 24 V power supply, what is the current flowing through the light bulb according to Ohm's law?

<p>2 A (A)</p> Signup and view all the answers

Find the electrostatic force between charges of +5.0 C and +3.0 C separated by a distance of 75 m in a vacuum.

<p>2.4 x 107 N (A)</p> Signup and view all the answers

In an electrical circuit with a resistor made of Ohmic material, the resistance is 10 Ω, and the voltage across the resistor is 20 V. What is the current flowing through the resistor?

<p>2 A (A)</p> Signup and view all the answers

If the charge of a dust particle trapped by an air purifier is increased, what will happen to the electric flux through a Gaussian surface surrounding the particle?

<p>The electric flux will increase. (C)</p> Signup and view all the answers

A circuit carries a constant current of 2 A for 10 seconds. What is the total charge transferred during this time?

<p>20 C (D)</p> Signup and view all the answers

What is the electric flux through a Gaussian surface surrounding a toner particle with a charge of -5 μC in a photocopier?

<p>It is negative because the toner particle has a negative charge. (C)</p> Signup and view all the answers

A flat surface with an area of 4 m² is placed in a uniform electric field of 6 N/C. The surface is oriented at an angle of 30° to the electric field. What is the electric flux through the surface?

<p>12 Nm²/C (C)</p> Signup and view all the answers

A wire carries a current of 4 A for 5 seconds. What is the total charge transferred through the wire during this time?

<p>20 C (D)</p> Signup and view all the answers

A flat surface of area 2 m² is placed in a uniform electric field of 5 N/C. The surface is oriented perpendicular to the electric field. What is the electric flux through the surface?

<p>10 Nm²/C (C)</p> Signup and view all the answers

If the current in a circuit is doubled, what happens to the total charge transferred over a given time period?

<p>The total charge is doubled. (D)</p> Signup and view all the answers

A dust particle is trapped by an air purifier. The electric field surrounding the particle is increased. How does this affect the electric flux through a Gaussian surface surrounding the particle?

<p>The electric flux increases. (C)</p> Signup and view all the answers

What is the current flowing through the resistor if the voltage across it is 10V and the resistance is 20Ω?

<p>0.5 A (C)</p> Signup and view all the answers

Two charges of +8.0 C and -6.0 C attract each other with a force of 3.0 x 10^3 N in a vacuum. What is the distance between the charges?

<p>1.6 x 10^7 m (B)</p> Signup and view all the answers

Which of the following best describes the relationship between current, voltage, and resistance in Ohmic materials, according to Ohm's law?

<p>The current is directly proportional to the voltage and inversely proportional to the resistance. (D)</p> Signup and view all the answers

Two small charged objects, q1=+5 μC, and q2=−3 μC, are placed 4 m apart on a straight line to create an electric field for a sensor. The sensor is located at a point, which is 2 m from q1 and 2 m from q2. What is the net electric field experienced by the sensor at this point?

<p>1.8×10^4 N/C (C)</p> Signup and view all the answers

A current of 0.25 A flows through a conductor for 2 hours, and the same current flows through another conductor for 5 hours. Which conductor experiences a greater total charge transfer?

<p>The conductor with 0.25 A for 5 hours transfers more charge. (C)</p> Signup and view all the answers

A charge q0=+1 μC is placed at the origin of a coordinate system. Two other charges, q1=+2 μC and q2=−3 μC are located at points (2 m, 0) and (0,3 m), respectively. Which of the following steps is incorrect in determining the net force on q0 due to q1 and q2?

<p>Add the magnitudes of the forces due to q1 and q2 directly without considering their directions. (B)</p> Signup and view all the answers

A current of 4 A flows through a conductor for 10 minutes. How much charge has flowed through the conductor during this time?

<p>2400 C (D)</p> Signup and view all the answers

A 100 Ω resistor is connected to a 12 V battery. The current flowing through the resistor is:

<p>0.12 A (A)</p> Signup and view all the answers

What describes the electric potential at a point due to a positive point charge?

<p>The electric potential decreases as the distance from the charge increases. (A)</p> Signup and view all the answers

How do capacitors play a role in signal processing applications?

<p>They filter out unwanted frequencies, allowing only the desired signal to pass. (D)</p> Signup and view all the answers

What is the electric potential at a point halfway between two equal and opposite charges +Q and −Q?

<p>The electric potential is zero. (D)</p> Signup and view all the answers

What is the function of capacitors in filtering circuits?

<p>Capacitors smooth out fluctuations in voltage by storing and releasing charge. (C)</p> Signup and view all the answers

Why are capacitors essential in timing circuits?

<p>To control the rate at which the circuit charges and discharges, determining the timing cycle. (B)</p> Signup and view all the answers

If the distance between two charges is doubled, how is the electric potential energy of the system affected?

<p>The electric potential energy is reduced by a factor of four. (D)</p> Signup and view all the answers

Why are capacitors used in power supply circuits?

<p>To store and release electrical energy to smooth out fluctuations in voltage. (C)</p> Signup and view all the answers

How does the strength of the electric field change when the distance from a point charge is doubled?

<p>The electric field strength is reduced by a factor of four. (B)</p> Signup and view all the answers

What describes the direction of the electric field created by a positive point charge?

<p>The electric field points radially outward from the charge. (C)</p> Signup and view all the answers

What occurs when a dielectric material is inserted between the plates of a charged capacitor?

<p>The capacitance increases, the charge on the plates remains the same, and the electric field decreases. (D)</p> Signup and view all the answers

What best describes the nature of the electric field between two parallel plates connected to a battery?

<p>The electric field is uniform and points from the positive plate to the negative plate. (B)</p> Signup and view all the answers

Why are capacitors preferred in a camera's flash unit for energy storage?

<p>Capacitors can release the stored energy quickly to generate a high-intensity flash. (C)</p> Signup and view all the answers

Which change occurs when the capacitance of a capacitor increases while the voltage remains constant?

<p>The charge on the capacitor increases. (D)</p> Signup and view all the answers

What is the effect of increasing voltage while keeping capacitance constant on a capacitor's charge?

<p>The charge on the capacitor increases. (D)</p> Signup and view all the answers

What happens to the electric field between two plates of a capacitor when the distance between the plates is increased?

<p>The electric field strength decreases. (C)</p> Signup and view all the answers

What does the equation $Q = I \times t$ represent in terms of electric current?

<p>The total amount of charge passing through a conductor in a given time. (A)</p> Signup and view all the answers

How does the electric flux change if a spherical surface surrounding a point charge is doubled in radius?

<p>The electric flux remains the same because it depends only on the enclosed charge. (A)</p> Signup and view all the answers

What will happen to the charge, capacitance, and voltage across the plates when a dielectric with a dielectric constant of 2 is inserted into a capacitor charged to 10V?

<p>The capacitance increases to 10 µF, the charge increases to 100 µC, and the voltage remains at 10 V. (B)</p> Signup and view all the answers

Which of the following factors does not affect the strength of the electric field created by a point charge?

<p>The presence of other charges nearby. (B)</p> Signup and view all the answers

What effect does disconnecting a capacitor from the power supply have when a dielectric with a dielectric constant of 4 is inserted?

<p>The capacitance increases to 40 µF, the charge remains at 60 µC, and the voltage decreases to 1.5 V. (D)</p> Signup and view all the answers

When is the electric flux through a surface equal to zero?

<p>When the surface is perpendicular to the electric field. (C)</p> Signup and view all the answers

What happens to the electric flux if the surface's orientation is changed from perpendicular to parallel with the electric field?

<p>The electric flux becomes zero. (C)</p> Signup and view all the answers

What is the outcome when the capacitance of a capacitor charged at a certain voltage is increased due to the insertion of a dielectric while being connected to a battery?

<p>The capacitance increases but the charge does not change. (B)</p> Signup and view all the answers

Flashcards

Ohm's Law

Relationship between current, voltage, and resistance.

Electric Force

The force between two charges due to their electric field.

Current Flow

Rate of electric charge passing a point in a circuit.

Charge Transfer

Total electric charge moved over time in a circuit.

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Coulomb's Law

Defines the force between two point charges.

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Electric Field

A field around charged objects affecting other charges.

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Vector Addition in Forces

Combining forces by considering their directions.

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Conductor Behavior

How different conductors respond to electric current.

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Superposition Principle

Calculates net electric field from multiple charges by summing vector contributions.

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Resistance and Length

Resistance increases as the length of a wire increases, due to longer pathways for current.

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Resistance and Cross-sectional Area

Resistance decreases as the cross-sectional area of a wire increases, providing more routes for current.

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Electric Field Calculation

Use Coulomb’s law to find electric fields and vector addition to sum them at a point.

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Doubling Length & Halving Area

Resistance of a wire increases by a factor of 4 if length is doubled and area is halved, according to R=ρ L/A.

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Ohm's Law Current

Current through a light bulb is calculated as I=V/R, where V=24V and R=12Ω gives 2A.

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Electrostatic Force Calculation

Finds the electrostatic force between two charges using Coulomb's law. Separation increases force's distance sensitivity.

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Resistance in Circuits

In a circuit, resistance, voltage, and current are related by Ohm's law: V=IR.

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Electric Flux

The electric field passing through a surface, representing how much field penetrates that surface.

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Zero Electric Flux

Occurs when a surface is perpendicular to the electric field lines.

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Equation Q=I × t

Represents the total charge (Q) passing through a conductor in a specific time (t) given the current (I).

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Effect of Radius on Electric Flux

Electric flux remains the same when the radius of a spherical surface is changed, as it depends only on the enclosed charge.

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Capacitance with Dielectric

When a dielectric is inserted in a charged capacitor, its capacitance increases, maintaining the same charge and voltage.

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Electric Field Strength Factors

Strength of the electric field depends on the magnitude of charge and distance; the medium affects it too, but nearby charges do not affect it.

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Voltage and Capacitance Change

In a disconnected charged capacitor, inserting a dielectric increases capacitance but reduces voltage while charge stays the same.

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Effect of Doubled Radius on Electric Flux

Doubling the radius of a spherical surface around a point charge does not change the electric flux.

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Capacitance

The ability of a capacitor to store charge per unit voltage.

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Electric Field Direction

The direction of an electric field created by a positive charge points radially outward.

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Electric Field Strength Change

When the distance from a point charge is doubled, the electric field strength is reduced by a factor of four.

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Dielectric in Capacitor

Inserting a dielectric increases capacitance, decreases charge, and reduces electric field.

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Parallel Plate Electric Field

The electric field between two parallel plates is uniform and points from positive to negative.

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Capacitors in Camera Flash

Capacitors are used in flash units because they release stored energy quickly for a high-intensity flash.

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Effect of Voltage on Capacitance

Capacitance can increase while charge remains the same if voltage remains constant.

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Charge on Capacitors

The charge on the plates of a capacitor can decrease when a dielectric is introduced with constant voltage.

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Electric potential due to positive charge

The electric potential increases as the distance from the charge increases.

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Importance of capacitors in signal processing

Capacitors filter out unwanted frequencies, allowing only the desired signal to pass.

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Electric potential between equal and opposite charges

The electric potential is zero at a point halfway between +Q and -Q.

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Capacitors in filtering circuits

Capacitors smooth out fluctuations in voltage by storing and releasing charge.

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Capacitors in timing circuits

Capacitors control the rate of charging and discharging, determining the timing cycle.

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Effect of distance on electric potential energy

If the distance between two charges is doubled, the electric potential energy is reduced by a factor of four.

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Capacitors in power supply circuits

Capacitors store and release electrical energy to smooth out fluctuations in voltage.

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Electric potential energy concepts

Electric potential energy relates inversely to the square of the distance between charges.

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Gaussian Surface

An imaginary closed surface surrounding a charge for analysis.

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Charge Transfer Equation Q=I × t

This equation calculates total electric charge transferred over time.

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Proportionality of Charge and Time

Total charge increases when current flows longer with constant current.

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Effect of Particle Charge on Electric Flux

Electric flux is determined by the charge within the Gaussian surface, not surrounding charges.

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Electric Field Strength

The strength of the electric force per unit charge in a field.

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Influence of Surface Orientation on Electric Flux

Electric flux is maximum when surface is parallel to the electric field direction.

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Current in Circuit Example (3 A for 5 sec)

Total charge transferred is calculated as 15 C from Q=I × t using values provided.

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Study Notes

Series and Parallel Circuits

  • Two resistors (10 Ω and 20 Ω) connected in series to a 30V battery, then in parallel with the same battery.
  • The total current in the parallel circuit is greater than in the series circuit.

Charging by Rubbing

  • When an object becomes charged by rubbing, electrons transfer between objects.

Kirchhoff's Current Law (KCL)

  • The total current entering a junction equals the total current leaving the junction.

Charging by Induction

  • Rearranging charges in an object without direct contact.

Wire Resistance

  • A wire with resistance of 8 Ω.
  • If the wire's length doubles and cross-sectional area halves, the new resistance becomes 32 Ω.

Rubbing vs. Induction

  • Rubbing involves direct contact; induction does not.

Resistance Formula and Wire Changes

  • Resistance (R) is related to resistivity (p), length (L), and cross-sectional area (A) by the formula: R = pL/A.
  • If the length of a wire is halved and its cross-sectional area is doubled, the resistance of the wire will be halved.

Net Electric Field

  • The net electric field at a point due to multiple charges is calculated by the superposition principle, summing vector contributions from each charge.

Resistance, Length, and Area

  • Resistance of a wire decreases as its cross-sectional area increases (according to R = pL/A).

Electric Field Calculation

  • To calculate the electric field at a point midway between two charges (+2C and -3C, separated by 4m), use Coulomb's law to find the field vectors due to each charge and then add them using vector addition.

Electric Field and Distance Change

  • Doubling the distance between charges reduces the electric field strength by a factor of four.

Charge and Electric Field

  • A point charge's electric field strength is affected by charge magnitude, proximity, and medium (surrounding material).

Current and Charge Transfer

  • A current of 0.25 A flowing through a conductor for 2 hours transfers less charge than the same current flowing for 5 hours.
  • Total charge = current x time.

Net Force Calculation

  • To find the net force on a charge due to other charges, calculate the force due to each charge using Coulomb's law and combine the forces using vector addition (considering both magnitude and direction).
  • Incorrect step: Adding the magnitudes of forces directly without considering their directions.

Current and Time

  • If current is doubled while keeping time constant in Q=I x t, the total charge transferred will double.

Electric, Flux, and Gaussian Surface

  • Electric flux depends only on the enclosed charge within the Gaussian surface, not the radius of the surface or the electric field strength.
  • In cases involving uniform electric field such as photocopiers, the electric flux is unaffected by the shape, surface size, or other factors within the uniform field, but relies only on the charge within the Gaussian surface.

Capacitor in Flash Unit

  • Capacitors are preferred in camera flash units for their ability to quickly release stored energy, generating a high-intensity flash.

Electric Potential

  • Electric potential at a point due to a positive point charge decreases as the distance from the charge increases.

Capacitors in Signal Processing

  • Capacitors are used in signal processing to filter out unwanted frequencies, allowing only desired signals to pass through. They smooth out voltage fluctuations by storing and releasing charge, and are not used for resistors in current control, or magnetic energy storage/release.

Electric Potential between Equal Opposite Charges

  • Electric potential at the midpoint between two equal and opposite charges is zero.

Capacitor in Timing Circuits

  • Used to control charge and discharge rate in timing circuits of oscillators and clocks.

###Electric Potential Energy and Distance

  • Doubling the distance between two charges reduces the electric potential energy of the system by a factor of 4.

Capacitor in Power Supply Circuits

  • Capacitors smooth out voltage fluctuations in electronic devices.

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