Physics · Class 9-10 · CBSE
Electric Current, Resistance and Ohm’s Law
Complete guide to electric charge, current (I = Q/t), potential difference (V = W/Q), Ohm’s law, factors determining resistance, series vs parallel circuits, and Joule’s heating effect.
1Electric Current and Potential Difference
Electric Current (I)is the rate of flow of electric charge through a conductor: I = Q / t (Unit: Ampere, A).Electric Potential Difference (V)is work done in moving a unit positive charge between two points: V = W / Q (Unit: Volt, V).
Ohm’s Law at Constant Temperature
- V = Potential difference across conductor (Volts)
- I = Current flowing through conductor (Amperes)
- R = Resistance of the conductor (Ohms, Ω)
Factors Affecting Resistance: R = ρ · (l / A)
| Factor | Relationship | Explanation |
|---|---|---|
| Length of Conductor (l) | R ∝ l | Longer wire causes more collisions for drifting electrons |
| Cross-Sectional Area (A) | R ∝ 1/A | Thicker wire provides wider highway, reducing collision density |
| Nature of Material (ρ) | R ∝ ρ (Resistivity) | Metals have low ρ (10⁻⁸ Ω·m), insulators have high ρ (10¹² Ω·m) |
| Temperature | R increases with T in metals | Thermal agitation of ions scatters flowing electrons more frequently |
Length of Conductor (l)
- Relationship
- R ∝ l
- Explanation
- Longer wire causes more collisions for drifting electrons
Cross-Sectional Area (A)
- Relationship
- R ∝ 1/A
- Explanation
- Thicker wire provides wider highway, reducing collision density
Nature of Material (ρ)
- Relationship
- R ∝ ρ (Resistivity)
- Explanation
- Metals have low ρ (10⁻⁸ Ω·m), insulators have high ρ (10¹² Ω·m)
Temperature
- Relationship
- R increases with T in metals
- Explanation
- Thermal agitation of ions scatters flowing electrons more frequently
2Series vs Parallel Circuit Combinations
Resistors can be connected inSeries(single path, same current) or inParallel(multiple branches, same potential difference).
Series vs Parallel Circuits: Complete Comparison
| Feature | Series Combination | Parallel Combination |
|---|---|---|
| Equivalent Resistance | R_eq = R₁ + R₂ + R₃ (always greater than max resistor) | 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ (smaller than min resistor) |
| Current Flow | Identical through every resistor: I_total = I₁ = I₂ | Current divides across branches: I_total = I₁ + I₂ + I₃ |
| Voltage / PD | Divides: V_total = V₁ + V₂ + V₃ | Identical across all parallel branches: V_total = V₁ = V₂ |
| Fault Impact | If one bulb blows, entire circuit breaks and shuts off | If one appliance fails, others continue working normally |
| Domestic Wiring Use | Not suitable for homes (used in fairy string lights) | Standard for household appliances (each gets full 220 V) |
Equivalent Resistance
- Series Combination
- R_eq = R₁ + R₂ + R₃ (always greater than max resistor)
- Parallel Combination
- 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ (smaller than min resistor)
Current Flow
- Series Combination
- Identical through every resistor: I_total = I₁ = I₂
- Parallel Combination
- Current divides across branches: I_total = I₁ + I₂ + I₃
Voltage / PD
- Series Combination
- Divides: V_total = V₁ + V₂ + V₃
- Parallel Combination
- Identical across all parallel branches: V_total = V₁ = V₂
Fault Impact
- Series Combination
- If one bulb blows, entire circuit breaks and shuts off
- Parallel Combination
- If one appliance fails, others continue working normally
Domestic Wiring Use
- Series Combination
- Not suitable for homes (used in fairy string lights)
- Parallel Combination
- Standard for household appliances (each gets full 220 V)
3Joule’s Law of Heating and Electric Power
When current flows through a purely resistive conductor, electrical energy is converted into thermal energy. This isJoule’s Heating Effect.
Joule’s Heat Formula
Practical Applications of Heating Effect
| Device | Element Used | Why Special Material is Chosen? |
|---|---|---|
| Electric Iron / Toaster | Nichrome alloy (Ni-Cr-Mn-Fe) | High resistivity and does not oxidize (burn) at red heat |
| Incandescent Bulb | Tungsten filament | Extremely high melting point (3380°C) allows glowing white hot |
| Electric Fuse | Lead-tin alloy wire | Low melting point melts safely when current exceeds rated threshold |
Electric Iron / Toaster
- Element Used
- Nichrome alloy (Ni-Cr-Mn-Fe)
- Why Special Material is Chosen?
- High resistivity and does not oxidize (burn) at red heat
Incandescent Bulb
- Element Used
- Tungsten filament
- Why Special Material is Chosen?
- Extremely high melting point (3380°C) allows glowing white hot
Electric Fuse
- Element Used
- Lead-tin alloy wire
- Why Special Material is Chosen?
- Low melting point melts safely when current exceeds rated threshold
4Exam Corner: Tips, Mistakes & Board Questions
Must-Remember Exam Points
- Ammeter is always connected in series (has very low resistance).
- Voltmeter is always connected in parallel across the component (has very high resistance).
- Alloys like nichrome and manganin have higher resistivity than constituent pure metals and do not oxidise readily at high temperatures.
Exam question · CBSE Class 10 Board
- A.18 Ω
- B.4 Ω
- C.2 Ω
- D.9 Ω
- Formula for parallel resistors: 1/R_eq = 1/R₁ + 1/R₂.
- Inverting gives R_eq = 4 Ω.
- Correct answer is option B (4 Ω).
Answer: B. 4 Ω
Remember
- Ohm’s law: ==V = IR== holds true for ohmic conductors at constant temperature.
- Resistance is given by ==R = ρ(l/A)==; depends on length, area, material, and temperature.
- Parallel circuits maintain equal220Vacross home appliances and prevent single-point failure.
- Joule heating: ==H = I²Rt== powers heaters, geysers, and safety fuses.
Check yourself
Question 1
If a wire of resistance R is stretched to double its original length, its new resistance will be: