Lesson Overview

Unit 7 covers electric current, resistance, resistivity, Ohm’s law, power, energy, electromotive force (emf), internal resistance, Kirchhoff’s laws, potentiometer, Wheatstone bridge, and application circuits. This unit forms the foundation of all electrical circuit analysis.

1. Core Concepts (Short Notes)

7.1 Electric Current (I)

• Flow of electric charge per unit time.

• I = Q/t.

• Unit: ampere (A).

• Conventional current flows from + to –.

7.2 Potential Difference (V)

• Work done per unit charge.

• V = W/Q.

7.3 Resistance (R)

• Opposition to the flow of current.

• R = V/I (Ohm’s law region).

• Unit: ohm (Ω).

7.4 Resistivity (ρ)

• Material property.

• R = ρL/A.

• ρ increases with temperature in metals.

7.5 Electromotive Force (emf)

• Energy supplied per unit charge by a source.

• E = V + Ir (including internal resistance r).

7.6 Power & Energy

• P = VI.

• Useful forms:

  • P = I²R

  • P = V²/R

• Electrical energy: E = Pt.

7.7 Kirchhoff’s Laws

1. Junction rule (KCL): ΣI(in) = ΣI(out).

2. Loop rule (KVL): Σ(emf) = Σ(IR) around a loop.

7.8 Potential Divider

• Vout = (R₂ / (R₁+R₂)) × Vin.

• Used for sensors and controlling voltage.

7.9 Wheatstone Bridge

• Balanced condition: R₁/R₂ = R₃/R₄.

7.10 Potentiometer

• Measures emf accurately.

• Based on potential drop along a uniform wire.

2. Detailed Notes for Each Section

7.1 Electric Current

Definition

Microscopic View

• I = nAve.

• n: number of free electrons.

• A: cross-sectional area.

• vₑ: drift velocity.

7.2 Potential Difference

V = W/Q.

• 1 volt = 1 joule per coulomb.

7.3 Resistance & Resistivity

Ohm’s Law

Temperature Effects

• Metals: R increases.

• Semiconductors: R decreases.

Resistivity Equation

R = ρL/A.

7.4 Power & Energy

Formulas

P = VI.P = I²R.P = V²/R.

Energy Consumption

E = Pt (kWh used in billing).

7.5 Emf & Internal Resistance

Terminal Voltage

Graphical Method

Plot V vs I.

• Intercept = E.

• Slope = –r.

7.6 Series & Parallel Circuits

Series

• I same.

• V divides.

• Rₑ = R₁ + R₂ + ...

Parallel

• V same.

• I divides.

• 1/Rₑ = 1/R₁ + 1/R₂ + ...

7.7 Kirchhoff’s Laws

KCL

Sum of currents at a junction = 0.

KVL

Sum of all emf = sum of all IR drops.

Applications

• Multi-loop circuits.

• Complex resistor networks.

7.8 Wheatstone Bridge

Balanced Condition:

Use

• Measuring unknown resistances.

• Sensitive and accurate.

7.9 Meter Bridge

Principle

Based on Wheatstone bridge.

Formula

7.10 Potentiometer

Principle

Uniform potential gradient.

Uses

• Comparing emf.

• Internal resistance measurement.

3. Formula Summary (Unit 7)

• I = Q/t

• V = W/Q

• R = V/I

• R = ρL/A

• P = VI = I²R = V²/R

• E = Pt

• V = E – Ir

• Rₛ = R₁ + R₂ + ...

• 1/Rₚ = 1/R₁ + 1/R₂ + ...

• KVL: ΣIR = Σemf

• Wheatstone bridge: R₁/R₂ = R₃/R₄

• Meter bridge: R = (l₁/l₂)R₀

4. Common Mistakes to Avoid

• Incorrect sign when applying KVL.

• Forgetting temperature effect on resistivity.

• Mixing parallel/series formulas.

• Using emf instead of potential difference in power formulas.

• Not ensuring Wheatstone bridge balance before calculation.

5. Exam Tips

• Always draw circuit diagrams neatly.

• Use arrows for current direction.

• When stuck, apply KCL first, then KVL.

• Potentiometer: use null point for accurate results.

• Show correct working and units.

6. Quick Revision Table