Full Physics Short Notes (Part 2) – Current Electricity to Magnetism & Matter | Class 12 & JEE 2026

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🔖 Full Physics Short Notes (Part 2)|Class 12 Physics & JEE 2026

The chapter Current Electricity deals with the flow of electric charge, resistance, drift velocity, Ohm’s law, resistivity, grouping of cells, Kirchhoff’s laws, Wheatstone bridge, potentiometer, and meter bridge. It is one of the most important scoring chapters for CBSE Class 12, JEE Main, NEET, and all competitive exams.

The chapter Magnetism and Matter explains magnetic materials, magnetic field quantities, bar magnet properties, hysteresis, Earth’s magnetism, and formulas essential for Boards and JEE.

✅ Section 1 - Current Electricity 

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🔵 1. Electric Current

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

Average current:

\[ I_{\text{av}} = \frac{\Delta q}{\Delta t} \]

Instantaneous current:

\[ I = \lim_{\Delta t \to 0} \frac{\Delta q}{\Delta t} = \frac{dq}{dt} \]

SI unit: Ampere (A)

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🔵 2. Current in a Conductor

\[ I = nqA v_d \]

Where:

• ( n ) = number of charge carriers per unit volume

• ( q ) = charge of electron

• ( A ) = area of cross-section

• ( \( v_d \) ) = drift velocity

Drift velocity:

\[ v_d = \frac{eE\tau}{m} \]

Where τ = relaxation time.

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🔵 3. Current Density (J) and Mobility (μ)

Current Density:

\[ \vec{J} = \frac{I}{A} \]

Also:

\[ J = \frac{n e^2 \tau}{m} E \]

Mobility:

\[ \mu = \frac{v_d}{E} = \frac{e \tau}{m} \]

Unit: m²/V·s

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🔵 4. Ohm’s Law & Resistance (R)

From drift velocity concept:

\[ I = \frac{n e^2 A \tau}{m} \cdot \frac{V}{l} \]

Thus:

\[ V = IR \]

Where resistance:

\[ R = \rho \frac{l}{A} \]

Resistivity:

\[ \rho = \frac{m}{n e^2 \tau} \]

Conductivity:

\[ \sigma = \frac{1}{\rho} \]

Units:

• R → ohm (Ω)

• ρ → Ω·m

• σ → Ω⁻¹·m⁻¹
  

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🔵 5. Temperature Dependence of Resistance

\[ R = R_0 \big( 1 + \alpha (T - T_0) \big) \]

Where α = temperature coefficient of resistivity

• Positive for conductors

• Negative for semiconductors
  

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🔵 6. Electrical Power & Heating Effect

\[ P = VI = I^2 R = \frac{V^2}{R} \]

Heat produced in time t:

\[ H = I^2 R t = V I t \]

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🔵 7. Kirchhoff’s Laws

1. Junction Law (KCL)

Sum of currents entering = sum of currents leaving.

\[ \sum I_{\text{in}} = \sum I_{\text{out}} \]

2. Loop Law (KVL)

Sum of all voltages in a closed loop is zero.

\[ \sum IR + \sum \text{EMF} = 0 \]

Direction rule:

• Entering higher potential → +

• Entering lower potential → –
  

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🔵 8. Combination of Resistances

⭐ Series:

\[ R = R_1 + R_2 + \dots + R_n \] ⭐ Parallel:

\[ \frac{1}{R_{\text{eq}}} = \sum_{n=1}^{n} \frac{1}{R_n} \]

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🔵 9. Wheatstone Bridge

Balanced condition:

\[ \frac{R_1}{R_2} = \frac{R_3}{R_4} \]

No current flows through galvanometer when balanced.

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🔵 10. Grouping of Cells

⭐ Series grouping

\[ E_{\rm eq} = E_1 + E_2 + \dots \] \[ r_{\rm eq} = r_1 + r_2 + \dots \]

⭐ Parallel grouping

\[ E_{\rm eq} = \frac{\frac{E_1}{r_1} + \frac{E_2}{r_2} + \dots}{\frac{1}{r_1} + \frac{1}{r_2} + \dots} \] \[ \frac{1}{r_{\rm eq}} = \frac{1}{r_1} + \frac{1}{r_2} + \dots + \frac{1}{r_n} \]

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🔵 11. Ammeter

A galvanometer + shunt resistor (S) connected in parallel.

For conversion:

\[ I_G R_G = (I - I_G) S \]

If \( I \gg I_G \) :

\[ S \approx \frac{I_G R_G}{I} \]

Ideal ammeter → zero resistance.

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🔵 12. Voltmeter

Galvanometer + high resistance ( \( R_S \) ) in series.

\[ V = I_G (R_S + R_G) \]

If \( R_S \gg R_G \) :

\[ R_S \approx \frac{V}{I_G} \]

Ideal voltmeter → infinite resistance.

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🔵 13. Potentiometer

Used to measure EMF, compare EMFs, find internal resistance, and measure small voltages.

Potential gradient:

\[ x = \frac{V}{L} \]

Applications:

✔ (a) Compare EMFs:

\[ \epsilon_1 = x l_1, \quad \epsilon_2 = x l_2 \] \[ \frac{\epsilon_1}{\epsilon_2} = \frac{l_1}{l_2} \]

✔ (b) Measurement of current:

\[ I = \frac{R_1 x}{l_1} \]

✔ (c) Internal resistance of a cell:

\[ \frac{\epsilon'}{\epsilon} = \frac{l_1}{l_2} \] \[ r = R\left(\frac{l_1}{l_2} - 1\right) \]

Potentiometer is an ideal voltmeter since it draws no current at balance.

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🔵 14. Meter Bridge

Used to find unknown resistance using balanced Wheatstone bridge principle.

If balance length = l:

\[ \frac{P}{Q} = \frac{l}{100 - l} \]

Where:

• P = resistance of wire AB

• Q = resistance of wire BC

Applying bridge condition:

\[ \frac{P}{Q} = \frac{R}{X} \quad \Rightarrow \quad X = R \cdot \frac{Q}{P} \]

Thus:

\[ X = R \cdot \frac{100 - l}{l} \]

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🟩 Short, Quick Revision Notes

• \(I = n q A v_d\)

• \( v_d = \frac{eE\tau}{m} \)

• \( J = \sigma E \)

• \( V = IR \)

• \( R = \rho l/A \), \( \sigma = 1/\rho \)

• \( P = I^2R \)

• Kirchhoff’s laws: KCL & KVL

• Series/Parallel resistance formulas

• Balanced Wheatstone → \( R_1/R_2 = R_4/R_3 \)

• Potentiometer → ideal voltmeter

• Meter bridge → \( X = R\frac{100-l}{l} \)

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✅ Section 2 - Magnetism and Matter 

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🔵 1. Important Magnetic Quantities

⭐ (A) Magnetic Field (B)

Magnetic field represents the total number of magnetic lines of force crossing per unit area.

Measured in tesla (T).

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⭐ (B) Magnetizing Field (H)

\[
\vec{H} = \frac{\vec{B}}{\mu}
\]

• H depends only on the source (current or magnet).

• Independent of the medium.

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⭐ (C) Intensity of Magnetization (I)

\[
I = \frac{\text{Magnetic Moment}}{\text{Volume}} = \frac{M}{V}
\]

Indicates how strongly a material gets magnetised.

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⭐ (D) Magnetic Susceptibility (χ)

\[
\chi = \frac{I}{H}
\]

Shows how easily a material can be magnetised.

• Positive → paramagnetic, ferromagnetic

• Negative → diamagnetic

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⭐ (E) Magnetic Permeability (μ)

Measures how easily magnetic field penetrates the material.

\[
B = \mu_0 (H + I)
\]

• μ = permeability of medium

• μ₀ = permeability of free space

Relative Permeability:

\[
\mu_r = \frac{\mu}{\mu_0} = 1 + \chi
\]

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🔵 2. Magnetic Materials

Classifies materials into three types:

Property	Paramagnetic	Diamagnetic	Ferromagnetic
Magnetisation	Weak, along H	Weak, opposite H	Strong, along H
Susceptibility χ	0 < χ < 1	–1 ≤ χ < 0	Very large (~10³)
Relative μ	μr > 1	0 < μr < 1	μr >> 1
Temp. dependence	\( \chi \propto \frac{1}{T} \)	Independent of T	Follows Curie Law

Curie Law for ferromagnets:

\[
\chi = \frac{C}{T - T_C}
\]

• TC → Curie temperature

• Above TC, ferromagnets become paramagnetic
  

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🔵 3. Hysteresis Loop

When a ferromagnetic material is magnetised and demagnetised, the B–H graph forms a loop:

Key terms:

• Retentivity: Magnetisation left behind when external field becomes zero.

• Coercivity: Reverse magnetising field required to demagnetise completely.

• Area of loop: Energy loss per cycle (heat).
  

Applications:

• Soft iron → small coercivity (electromagnets)

• Steel → large coercivity (permanent magnets)

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🔵 4. Earth’s Magnetic Field

Three components of Earth’s magnetic field:

⭐ Components:

1. BH → Horizontal component

2. BV → Vertical component

3. BE → Earth’s total magnetic field

Relations:

\[
\tan \delta = \frac{B_V}{B_H}
\]

\[
B_H = B_E \cos \delta
\]

\[
B_E = \sqrt{B_H^2 + B_V^2}
\]

Where:

• δ = angle of dip

• q = angle of declination (between geographic & magnetic meridians)
  

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🔵 5. Bar Magnet

⭐ (A) Magnetic Field Due to Bar Magnet

Formulas for the axial and equatorial positions.

Let:

• M = magnetic moment

• l = half length of magnet

• d = distance from center

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⭐ (i) Axial Position (Point P)

Exact formula:

\[
B_P = \frac{\mu_0}{4\pi} \cdot \frac{2Md}{(d^2 - l^2)^2}
\]

If \( l^2 \ll d^2 \):

\[
B_P \approx \frac{\mu_0}{4\pi} \cdot \frac{2M}{d^3}
\]

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⭐ (ii) Equatorial Position (Point Q)

Exact:

\[
B_Q = \frac{\mu_0}{4\pi} \cdot \frac{M}{(d^2 + l^2)^{3/2}}
\]

If \( l^2 \ll d^2 \):

\[
B_Q \approx \frac{\mu_0}{4\pi} \cdot \frac{M}{d^3}
\]

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⭐ (iii) General Point at Angle θ

\[
B = \frac{\mu_0}{4\pi} \cdot \frac{M}{r^3} \sqrt{1 + 3\cos^2\theta}
\]

And:

\[
\tan\phi = \frac{1}{2}\tan\theta
\]

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🔵 6. Bar Magnet in a Uniform Magnetic Field

Important formulas:

⭐ (i) Torque:

\[
\vec{\tau} = \vec{M} \times \vec{B}
\]

Magnitude:

\[
\tau = MB\sin\theta
\]

⭐ (ii) Potential Energy:

\[
U = - \vec{M} \cdot \vec{B} = -MB\cos\theta
\]

⭐ (iii) Work Done in Rotating the Magnet:

\[
W = MB(\cos\theta_i - \cos\theta_f)
\]

⭐ (iv) Time Period of Small Oscillations:

\[
T = 2\pi \sqrt{\frac{I}{MB}}
\]

Where I = moment of inertia.

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🟩 Short Revision Notes

• Magnetic susceptibility (χ) decides how easily a material magnetises.

• Paramagnetic → weak, Diamagnetic → weak opposite, Ferromagnetic → very strong.

• Curie temperature: ferromagnets → paramagnets.

• Hysteresis: retentivity, coercivity, energy loss.

• Earth's field → declination (q), dip (δ), horizontal (BH), total (BE).

• Bar magnet fields ∝ 1/r³ at far distances.

• Torque = MB sinθ

• Potential energy = –MB cosθ

• Oscillation time ∝ √(I / MB)

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