Current Electricity 

Class 12 Physics – Chapter: Current Electricity – Notes

Introduction Current electricity deals with the study of electric charges in motion. It focuses on how electric current flows through conductors and how different components of an electrical circuit behave under various conditions. Understanding this chapter is crucial for scoring well in Class 12 board exams and also forms the backbone for competitive exams like JEE and NEET.

1. Electric Current

Definition: Electric current is the rate of flow of electric charge through a conductor.

Formula: I = Q / t Where:

• I = Current (Ampere)

• Q = Charge (Coulomb)

• t = Time (seconds)

SI Unit: Ampere (A) 1 A = 1 C/s

Direction of Current: Conventional current flows from the positive terminal to the negative terminal of a cell or battery.

Types of Current:

1. Direct Current (DC): Flows in one direction (e.g., from a battery).

2. Alternating Current (AC): Changes direction periodically (e.g., power supply from mains).

2. Electric Current in Conductors

Conductors: Materials that allow electric charges to flow easily (e.g., copper, aluminum).

Free Electrons: In conductors, free electrons are responsible for carrying current.

Drift Velocity (v_d): The average velocity of electrons under an electric field.

Formula: v_d = (e × E × τ) / m Where:

• e = Charge of electron

• E = Electric field

• τ = Relaxation time

• m = Mass of electron

Another important formula: v_d = I / (n × A × e) Where:

• n = Number of electrons per unit volume

• A = Cross-sectional area

• e = Electron charge

Current Density (J): J = I / A Also, J = σ × E (Where σ is electrical conductivity)

4. Resistance and Resistivity

Resistance (R): Opposition offered by a conductor to the flow of electric current.

Formula: R = ρ × (L / A) Where:

• ρ = Resistivity

• L = Length

• A = Cross-sectional Area

SI Unit of Resistance: Ohm (Ω)

Resistivity (ρ):

• A material property

• SI Unit: Ω m

Temperature Dependence of Resistance: R = R_0 (1 + α × ΔT) Where:

• α = Temperature coefficient of resistance

Conductivity (σ): σ = 1 / ρ

What is a Parallel Combination?

When resistors are connected side by side, such that both ends of each resistor are directly connected to the same two points, they are said to be in a parallel configuration.

Key Characteristics of a Parallel Circuit:

1. Same Voltage Across Each Resistor:

   • In a parallel circuit, all resistors experience the same voltage because they are all connected across the same two points (like the + and – terminals of a battery).

   • For example, if you connect three resistors in parallel to a 10V battery, each resistor gets 10 volts across it.

2. Current Divides Among Resistors:

   • The total current from the power source splits and flows through each resistor.

   • The amount of current through each resistor depends on its resistance. Resistors with lower resistance get more current, and those with higher resistance get less current.
     
     

How to Calculate the Equivalent Resistance (R_eq):

• The total or equivalent resistance in a parallel circuit is always less than the smallest resistor in the group.

• To find the equivalent resistance, use this formula:
  
  Parallel Combination: 1 / R_eq = 1 / R1 + 1 / R2 + 1 / R3 + ...

• Same voltage across each resistor

• Current divides

Eample:

Suppose you have three resistors:
R1 = 6 ohms, R2 = 3 ohms, and R3 = 2 ohms in parallel.

Step 1: Calculate reciprocals:
1 / 6 = 0.166
1 / 3 = 0.333
1 / 2 = 0.5

Step 2: Add them up:
0.166 + 0.333 + 0.5 = 0.999

Step 3: Take the reciprocal:
1 / 0.999 ≈ 1 ohm

So, the equivalent resistance is approximately 1 ohm.

What is a Series Combination?

When resistors are connected one after another in a single path, they are said to be in a series combination. In this setup, the same current flows through each resistor, like water flowing through a single pipe that goes through multiple valves.

Key Characteristics of a Series Circuit:

1. Same Current Through All Resistors:

   • There is only one path for the current to flow, so the same current passes through each resistor.

   • Think of it like a single-lane road: all the traffic must go through every checkpoint.

2. Voltage is Divided Among Resistors:

   • The total voltage from the power source is shared across all the resistors.

   • Resistors with higher resistance drop more voltage, and lower resistance ones drop less.

How to Calculate the Equivalent Resistance (R_eq):

• In a series combination, the total or equivalent resistance is simply the sum of all the resistors:
  
  R_eq = R1 + R2 + R3 + ...

• So you're just adding the resistances together, no reciprocals involved.

Example:

Suppose you have three resistors in series:
R1 = 4 ohms, R2 = 6 ohms, and R3 = 10 ohms

Then the equivalent resistance is:
R_eq = 4 + 6 + 10 = 20 ohms

So the total resistance of the circuit is 20 ohms.

7. EMF and Potential Difference

Electromotive Force (EMF): Total energy supplied per coulomb of charge by a source like a cell.

Formula: EMF (E) = Work done / Charge

Potential Difference (V): Energy used per unit charge to move it between two points in a circuit.

8. Internal Resistance of a Cell

Definition: Resistance within the cell which resists the flow of current.

Formula: V = E - Ir Where:

• V = Terminal voltage

• E = EMF of cell

• I = Current

• r = Internal resistance

Factors Affecting Internal Resistance:

• Distance between electrodes

• Area of electrodes

• Nature of electrolyte

9. Cell Combination

Cells in Series: E_total = E1 + E2 + E3 + ... Internal resistance adds up: r_total = r1 + r2 + r3 + ...

Cells in Parallel: E_total = (E1 / r1 + E2 / r2 + ...) / (1 / r1 + 1 / r2 + ...)

10. Kirchhoff’s Laws

1. Kirchhoff’s Current Law (KCL): Total current entering a junction = Total current leaving the junction.

2. Kirchhoff’s Voltage Law (KVL): Sum of the potential differences in a closed loop is zero.

Application: Used to analyze complex circuits that cannot be simplified using series-parallel rules.

11. Wheatstone Bridge

Purpose: Used to find unknown resistance.

Balanced Condition: (P / Q) = (R / S) Where:

• P, Q, R are known resistances

• S is unknown

12. Meter Bridge

Based on Wheatstone bridge principle. Used to determine unknown resistance using a 1-meter wire.

Formula: (R / S) = (l1 / l2) Where:

• l1 = Length from 0 to null point

• l2 = Remaining length of wire

13. Potentiometer

Working Principle: Based on potential drop across a uniform wire.

Applications:

• Compare EMFs of two cells

• Measure the internal resistance of a cell

Advantages Over Voltmeter:

• No current is drawn

• More Accurate

The formula for Comparing EMFs: E1 / E2 = l1 / l2

Formula for Internal Resistance: r = R × ((l1 - l2) / l2)

Current Electricity is a conceptually rich chapter combining theoretical and numerical understanding. It covers a variety of essential principles that not only serve well for board exams but are heavily used in real-life applications, engineering concepts, and higher studies. Practice numerical based on drift velocity, Ohm's Law, circuit analysis using Kirchhoff's laws, and problems involving resistors in circuits for thorough preparation.

 Stay tuned for more detailed breakdowns in other chapters!