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Class 12 Science (PCM)

Physics Part 1

Current Electricity

Current Electricity

Action PlanNotesQuestionsMock-Test
Study Action Plan (Sorted by Difficulty)
Complex Circuit Analysis Using Symmetry and Kirchhoff Rules
Accuracy: 0%
Total Attempted0
Total Correct0
Total Incorrect0
Difficulty Level:
High
Origin of Resistivity and Relaxation Time
Accuracy: 28%
Total Attempted18
Total Correct5
Total Incorrect13
Difficulty Level:
High
Limitations of Ohm’s Law and Non-ohmic Devices
Accuracy: 31%
Total Attempted16
Total Correct5
Total Incorrect11
Difficulty Level:
High
Power in Electrical Circuits
Accuracy: 33%
Total Attempted12
Total Correct4
Total Incorrect8
Difficulty Level:
High
Standard Resistor Materials
Accuracy: 50%
Total Attempted6
Total Correct3
Total Incorrect3
Difficulty Level:
Medium
Terminal Voltage and Charging/Discharging of Cells
Accuracy: 50%
Total Attempted6
Total Correct3
Total Incorrect3
Difficulty Level:
Medium
Wheatstone Bridge
Accuracy: 50%
Total Attempted6
Total Correct3
Total Incorrect3
Difficulty Level:
Medium
Cells, EMF, and Internal Resistance
Accuracy: 57%
Total Attempted21
Total Correct12
Total Incorrect9
Difficulty Level:
Medium
Ohm's Law and Resistance
Accuracy: 58%
Total Attempted19
Total Correct11
Total Incorrect8
Difficulty Level:
Medium
Resistivity of Conductors, Semiconductors and Insulators
Accuracy: 58%
Total Attempted12
Total Correct7
Total Incorrect5
Difficulty Level:
Medium
Kirchhoff's Circuit Laws
Accuracy: 60%
Total Attempted20
Total Correct12
Total Incorrect8
Difficulty Level:
Medium
Drift Velocity and Current Density
Accuracy: 65%
Total Attempted20
Total Correct13
Total Incorrect7
Difficulty Level:
Medium
Electric Current and Charge Flow
Accuracy: 69%
Total Attempted16
Total Correct11
Total Incorrect5
Difficulty Level:
Medium
Electric Current in Conductors
Accuracy: 69%
Total Attempted16
Total Correct11
Total Incorrect5
Difficulty Level:
Medium
Cells in Series and Parallel
Accuracy: 73%
Total Attempted15
Total Correct11
Total Incorrect4
Difficulty Level:
Medium
Current as Scalar and Current Density as Vector
Accuracy: 75%
Total Attempted12
Total Correct9
Total Incorrect3
Difficulty Level:
Low
Mobility of Charge Carriers
Accuracy: 75%
Total Attempted4
Total Correct3
Total Incorrect1
Difficulty Level:
Low
Resistance, Resistivity and Conductivity
Accuracy: 77%
Total Attempted13
Total Correct10
Total Incorrect3
Difficulty Level:
Low
Temperature Dependence of Resistivity
Accuracy: 83%
Total Attempted6
Total Correct5
Total Incorrect1
Difficulty Level:
Low
Electrical Units, Dimensions and Key Formula Summary
Accuracy: 100%
Total Attempted1
Total Correct1
Total Incorrect0
Difficulty Level:
Low

Learning Objectives

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Learning Objectives

  • Understand and apply Kirchhoff's Junction Rule in circuit analysis.
  • Understand and apply Kirchhoff's Loop Rule in circuit analysis.
  • Analyze the Wheatstone bridge and determine unknown resistances.
  • Define and calculate electric current, voltage, resistance, and resistivity.
  • Explain the limitations of Ohm's Law and identify materials that do not obey it.
  • Calculate current density and drift velocity in conductive materials.
  • Describe the relationship between electric field, drift velocity, and current density.
  • Identify the factors affecting resistance in conductors and their implications in circuit design.

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Revision Notes & Summary

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Chapter Notes on Current Electricity

1. Kirchhoff's Rules

  • Junction Rule: At any junction of circuit elements, the sum of currents entering the junction must equal the sum of currents leaving it.
  • Loop Rule: The algebraic sum of changes in potential around any closed loop must be zero.

2. Wheatstone Bridge

  • Arrangement of four resistances: R₁, R₂, R₃, R₄.
  • Null-point condition: R1/R2=R3/R4R_1 / R_2 = R_3 / R_4

3. Physical Quantities and Units

Physical QuantitySymbolDimensionsUnitRemark
Electric currentI[A]ASI base unit
ChargeQ,q[T A]C
Voltage, Electric potential differenceV[ML²T³A⁻¹]VWork/charge
Electromotive forceε[M L² T⁻³ A⁻¹]VWork/charge
ResistanceR[ML²T⁻³A⁻²]CR = V/I
Resistivityp[ML³T⁻³A⁻²]Ω mR = pl/A
Electrical conductivityσ[M⁻¹ L⁻³ T³ A²]Sσ = 1/p
Electric fieldE[M LT ³ A⁻¹]V m⁻¹Electric force charge
Drift speedv_d[LT⁻¹]m s⁻¹v_a = et
Relaxation timeτ[T]S
Current densityj[L⁻² A]A m⁻²current/area
Mobilityµm²V⁻¹s⁻¹v_a/E

4. Current and Charge Flow

  • Current is a scalar quantity, represented by an arrow.
  • The current I through an area of cross-section is given by the scalar product: I=jSI = j S

5. Ohm's Law and Limitations

  • Ohm's Law: V=IRV = IR is not universally applicable.
  • Limitations include:
    • V is not proportional to I.
    • Relation between V and I depends on the sign of V.
    • Non-unique relation between V and I.

6. Important Concepts

  • Drift Velocity: The average velocity of charge carriers in a conductor due to an electric field.
  • Resistivity: Depends on material and temperature.
  • Current Density: Amount of charge flowing per second per unit area.

7. Kirchhoff's Junction Rule

  • Based on conservation of charge; outgoing currents equal incoming currents at a junction.

8. Example Circuit Analysis

  • Example circuit with resistors and voltage sources illustrating Kirchhoff's rules and current flow.

9. Exercises

  • Problems related to current, resistance, and circuit analysis.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

V=I(R1+R2+R3)V = I(R_1 + R_2 + R_3)

B.

V=I(R1R2R3)V = I(R_1R_2R_3)

C.

V=I(R1+R2)V = I(R_1 + R_2)

D.

V=I(R1+R3)V = I(R_1 + R_3)
Correct Answer: A

Solution:

In a series circuit, the total voltage drop across the resistors is the sum of the individual voltage drops, which is V=I(R1+R2+R3)V = I(R_1 + R_2 + R_3).

Chapter Concept:

Kirchhoff's Circuit Laws

A.

5×104 S/m5 \times 10^4 \text{ S/m}

B.

5×103 S/m5 \times 10^3 \text{ S/m}

C.

5×102 S/m5 \times 10^2 \text{ S/m}

D.

5×101 S/m5 \times 10^1 \text{ S/m}
Correct Answer: B

Solution:

Conductivity σ\sigma is given by σ=jE\sigma = \frac{j}{E}. Substituting the given values, σ=5×10510=5×104 S/m\sigma = \frac{5 \times 10^5}{10} = 5 \times 10^4 \text{ S/m}.

Chapter Concept:

Resistance, Resistivity and Conductivity

A.

The equivalent emf is the sum of the individual emfs.

B.

The equivalent emf is the average of the individual emfs.

C.

The equivalent emf is the product of the individual emfs.

D.

The equivalent emf is the difference between the highest and lowest emf.
Correct Answer: A

Solution:

In a series combination, the equivalent emf is the sum of the individual emfs of the cells.

Chapter Concept:

Cells in Series and Parallel

A.

4.87 mA

B.

0 mA

C.

2.5 mA

D.

5 mA
Correct Answer: A

Solution:

Using Kirchhoff's rules for the given mesh equations, the current through the galvanometer is calculated to be 4.87 mA4.87 \, mA.

Chapter Concept:

Complex Circuit Analysis Using Symmetry and Kirchhoff Rules

A.

Resistor

B.

Diode

C.

Copper wire

D.

Nichrome wire
Correct Answer: B

Solution:

A diode is a non-ohmic device because its V-I relationship is non-linear and depends on the polarity of the applied voltage.

Chapter Concept:

Limitations of Ohm’s Law and Non-ohmic Devices

A.

The resistivity increases.

B.

The resistivity decreases.

C.

The resistivity remains unchanged.

D.

The resistivity first increases then decreases.
Correct Answer: B

Solution:

Resistivity is inversely proportional to the number of free electrons per unit volume nn. Increasing nn decreases the resistivity.

Chapter Concept:

Origin of Resistivity and Relaxation Time

A.

ρT=ρ0[1+α(T−T0)]\rho_T = \rho_0 [1 + \alpha (T - T_0)]

B.

ρT=ρ0[1−α(T−T0)]\rho_T = \rho_0 [1 - \alpha (T - T_0)]

C.

ρT=ρ0[1+α(T+T0)]\rho_T = \rho_0 [1 + \alpha (T + T_0)]

D.

ρT=ρ0[1−α(T+T0)]\rho_T = \rho_0 [1 - \alpha (T + T_0)]
Correct Answer: A

Solution:

The resistivity ρT\rho_T at temperature TT is given by ρT=ρ0[1+α(T−T0)]\rho_T = \rho_0 [1 + \alpha (T - T_0)], where α\alpha is the temperature coefficient of resistivity.

Chapter Concept:

Temperature Dependence of Resistivity

A.

The current II is approximately ε/R\varepsilon / R.

B.

The current II is approximately ε/(R+r)\varepsilon / (R + r).

C.

The current II is approximately ε/r\varepsilon / r.

D.

The current II is zero.
Correct Answer: A

Solution:

When R≫rR \gg r, the internal resistance can be neglected, and the current II is approximately ε/R\varepsilon / R.

Chapter Concept:

Cells, EMF, and Internal Resistance

A.

The terminal voltage is less than the emf.

B.

The terminal voltage equals the emf.

C.

The terminal voltage exceeds the emf.

D.

The terminal voltage is zero.
Correct Answer: C

Solution:

During charging, the terminal voltage can exceed the emf depending on the direction of the current, as the external voltage must overcome both the emf and the internal resistance.

Chapter Concept:

Terminal Voltage and Charging/Discharging of Cells

A.

Resistivity increases due to increased collision frequency.

B.

Resistivity decreases because the number of charge carriers increases.

C.

Resistivity remains constant as temperature changes.

D.

Resistivity decreases due to a decrease in collision frequency.
Correct Answer: B

Solution:

In semiconductors, as temperature increases, the number of charge carriers increases significantly, leading to a decrease in resistivity.

Chapter Concept:

Resistivity of Conductors, Semiconductors and Insulators

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Current Electricity

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True or False

Correct Answer: True

Solution:

Electric current is defined as the net charge crossing a given area per unit time. It can be positive or negative depending on the direction chosen for the current flow. This is consistent with the definition provided in the text.

Chapter Concept :

Electric Current and Charge Flow

Correct Answer: True

Solution:

Ohm's law is defined by the equation V=IRV = IR, indicating that the resistance RR is a constant for a given conductor, independent of VV and II, as long as the conductor exhibits linear V−IV-I behavior.

Chapter Concept :

Ohm's Law and Resistance

Correct Answer: True

Solution:

Electric current is indeed defined as the net charge crossing a given area per unit time. This is a fundamental definition in the study of electric currents.

Chapter Concept :

Electric Current and Charge Flow

Correct Answer: True

Solution:

The drift velocity vdv_d is given by vd=eEτmv_d = \frac{eE\tau}{m}, where EE is the electric field, indicating that vdv_d is directly proportional to EE.

Chapter Concept :

Drift Velocity and Current Density

Correct Answer: True

Solution:

The electromotive force (EMF) is defined as the potential difference between the positive and negative electrodes of a cell in an open circuit, i.e., when no current is flowing through the cell.

Chapter Concept :

Cells, EMF, and Internal Resistance

Correct Answer: True

Solution:

Ohm's law states that the current through an ohmic conductor is proportional to the potential difference across it, with the condition that the resistance remains constant and is independent of the voltage and current.

Chapter Concept :

Ohm's Law and Resistance

Correct Answer: True

Solution:

High-voltage transmission reduces power loss in cables because the power loss, given by Pc=I2RcP_c = I^2 R_c, is inversely proportional to the square of the voltage VV. By increasing the voltage, the current II can be reduced for the same power PP, thereby reducing the power loss in the cables.

Chapter Concept :

Power in Electrical Circuits

Correct Answer: True

Solution:

In semiconductors, the number of charge carriers increases with temperature, which decreases resistivity.

Chapter Concept :

Temperature Dependence of Resistivity

Correct Answer: True

Solution:

The EMF is defined as the potential difference between the positive and negative electrodes in an open circuit, i.e., when no current is flowing through the cell.

Chapter Concept :

Cells, EMF, and Internal Resistance

Correct Answer: True

Solution:

In solid conductors, the current is indeed carried by free electrons moving through a lattice of fixed positive ions, as stated in the provided text.

Chapter Concept :

Electric Current in Conductors

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