⚡ Electric Charge & Current
- Charge (Q): Fundamental property; SI unit coulomb (C).
- Charge is quantised: Q = n × e where e = 1.6 × 10⁻¹⁹ C.
- Electric current (I): Rate of flow of charge.
- I = Q / t · SI unit ampere (A) = 1 C/s.
- Conventional current flows opposite to electron flow.
- Measured by an ammeter connected in series.
🔋 Potential Difference
- Work done to move a unit charge between two points.
- V = W / Q · SI unit volt (V) = 1 J/C.
- A cell/battery maintains the potential difference that drives current.
- Current flows from high to low potential.
- Measured by a voltmeter connected in parallel.
Remember: Ammeter → series (low resistance). Voltmeter → parallel (high resistance).
📏 Ohm's Law
V = I R
- Current through a conductor ∝ potential difference across it, at constant temperature.
- V–I graph is a straight line through the origin.
- Slope of V–I graph = resistance R.
Ohmic conductors obey Ohm's law (metals). Non-ohmic do not (diode, filament bulb).
🔧 Resistance
R = V / I
- Property that opposes the flow of current.
- SI unit: ohm (Ω); 1 Ω = 1 V/A.
- A rheostat is a variable resistor used to change current.
- Good conductors → low R; insulators → very high R.
🧵 Resistivity & Factors
R = ρ L / A
- R ∝ length (L) — longer wire, more resistance.
- R ∝ 1 / area (A) — thicker wire, less resistance.
- Resistivity ρ = RA/L · SI unit ohm-metre (Ω·m).
- ρ depends only on material & temperature, NOT on dimensions.
- For metals, R increases with temperature.
Resistivity Values
| Material | ρ (Ω·m) | Type |
|---|
| Silver | 1.6 × 10⁻⁸ | Conductor |
| Copper | 1.7 × 10⁻⁸ | Conductor |
| Aluminium | 2.7 × 10⁻⁸ | Conductor |
| Nichrome | ~100 × 10⁻⁸ | Alloy |
| Rubber | 10¹³ – 10¹⁶ | Insulator |
Why Nichrome? High resistivity + high melting point → used in heaters & toasters. Copper/aluminium (low ρ) → used for wires.
🔗 Series vs Parallel Combination
Series
R = R₁ + R₂ + R₃ + …
- Same current through all resistors.
- Voltage divides: V = V₁ + V₂ + V₃.
- Total R is larger than largest resistor.
- One breaks → whole circuit stops.
Parallel
1/R = 1/R₁ + 1/R₂ + 1/R₃
- Same voltage across all resistors.
- Current divides: I = I₁ + I₂ + I₃.
- Total R is smaller than smallest resistor.
- One breaks → others keep working.
Household wiring uses parallel so every appliance gets 220 V and can be switched independently.
🔥 Heating Effect of Current
When current flows through a resistor, electrical energy converts to heat — Joule's Law of Heating.
H = I²Rt
- H ∝ I² (square of current).
- H ∝ R (resistance).
- H ∝ t (time).
Applications: Electric heater, iron, geyser, toaster, incandescent bulb, and the fuse (safety).
💡 Electric Power
P = V I = I²R = V²/R
- Rate of consuming electrical energy.
- SI unit: watt (W) = 1 J/s.
- 1 kilowatt (kW) = 1000 W.
- 1 horsepower (hp) = 746 W.
Bulb rating "60 W, 220 V": R = V²/P = 220²/60 ≈ 807 Ω.
🔌 Electrical Energy
Energy = Power × time
- SI unit: joule (J).
- Commercial unit: kilowatt-hour (kWh) = 1 "unit".
- 1 kWh = 3.6 × 10⁶ J
Bill example: A 1000 W heater for 2 h = 2 kWh = 2 units of electricity.
🧮 Key Formulas at a Glance
| Quantity | Formula | SI Unit |
|---|
| Current | I = Q/t | ampere (A) |
| Charge | Q = ne | coulomb (C) |
| Potential Difference | V = W/Q | volt (V) |
| Ohm's Law | V = IR | — |
| Resistance | R = ρL/A | ohm (Ω) |
| Series | R = R₁+R₂+… | ohm (Ω) |
| Parallel | 1/R = Σ 1/Rᵢ | ohm (Ω) |
| Heat | H = I²Rt | joule (J) |
| Power | P = VI = I²R = V²/R | watt (W) |
| Energy | E = Pt | kWh / joule |
🔣 Circuit Symbols
| Component | Symbol |
|---|
| Cell | ┤├ (long +, short −) |
| Battery | ┤├┤├ |
| Switch (open) | ─○ ○─ |
| Resistor | ▭ (box) |
| Variable resistor | ▭ with arrow |
| Ammeter | —(A)— |
| Voltmeter | —(V)— |
| Bulb | —⊗— |
🧠 Memory Tricks
- "V = IR" → "Volts Is Resistance" — Ohm's triangle: cover the unknown.
- Series adds, parallel reciprocates.
- Ammeter = series ("A" comes before "series" alphabetically — low R). Voltmeter = parallel (high R).
- "PIVR": P = VI, and also I²R and V²/R.
- Heat "I²Rt" — "I squared RT" (RT like room temperature).
- 1 unit = 1 kWh = 3.6 MJ.
⚠️ Common Board Mistakes
- ❌ Connecting an ammeter in parallel or a voltmeter in series.
- ❌ Adding resistances directly in parallel (must use reciprocals).
- ❌ Forgetting to convert cm/minutes; use SI units.
- ❌ Writing power as P = V/I (correct: P = VI).
- ❌ Confusing kW and kWh (power vs energy).
- ❌ Thinking thicker wire = more resistance (it's less).
- ❌ Forgetting H ∝ I² — doubling current gives 4× heat.
🎯 Worked Numericals
Combination Problem
Three resistors 2 Ω, 3 Ω, 6 Ω are connected in parallel across a 6 V battery. Find total R and total current.
Solution:
1/R = 1/2 + 1/3 + 1/6 = 6/6 = 1 ⟹ R = 1 Ω
I = V/R = 6/1 = 6 A total current.
Power & Energy Problem
An electric iron of 750 W works for 2 hours daily. Find energy used in 30 days and cost at ₹5/unit.
Solution:
E = 0.75 kW × 2 h × 30 = 45 kWh
Cost = 45 × ₹5 = ₹225.