Quick Summary
Electricity deals with charges in motion. This chapter is the highest-weightage science chapter for Tamil Nadu Class 10 board exams. You need to master definitions, Ohm's law, series and parallel circuit derivations, Joule's heating law, and a variety of numerical problems.
Key Definitions
- Electric current (I): Rate of flow of electric charge.
I = Q/t. SI unit: ampere (A). - Potential difference (V): Work done to move unit positive charge from one point to another.
V = W/Q. SI unit: volt (V). - Resistance (R): Opposition offered by a conductor to the flow of current. SI unit: ohm (Ω).
- Ohm's law: At constant temperature, V ∝ I, so V = IR.
- Electric power (P): Rate at which electrical energy is consumed.
P = VI. SI unit: watt (W). - Electric energy (E): Total energy consumed in a given time.
E = Pt. SI unit: joule (J) or kWh.
Formulae Reference
| Concept | Formula | SI Unit |
|---|---|---|
| Current | I = Q/t | ampere (A) |
| Potential difference | V = W/Q | volt (V) |
| Ohm's law | V = IR | — |
| Power | P = VI = I²R = V²/R | watt (W) |
| Energy | E = Pt | joule (J) or kWh |
| Joule's heating | H = I²Rt | joule (J) |
| Series resistance | R_total = R₁ + R₂ + R₃ | ohm (Ω) |
| Parallel resistance | 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ | ohm (Ω) |
Ohm's Law — Explained with Analogy
Statement: At constant temperature, the current (I) through a conductor is directly proportional to the potential difference (V) across its ends.
Water pipe analogy: Think of electric current as water flowing through a pipe.
A higher pressure (voltage) drives more water (current) through the same pipe (resistance).
- Potential difference = water pressure pushing the flow
- Current = rate of water flow
- Resistance = narrowness of the pipe (a narrow pipe has high resistance; a wide pipe has low resistance)
Limitations of Ohm's law:
- It holds only at constant temperature.
- It does not apply to semiconductors (diodes, transistors) or electrolytes.
- It fails when the conductor is heated significantly (resistance changes with temperature).
Resistance — Factors Affecting It
The resistance of a conductor depends on: 1. Length (L): R ∝ L — longer wire has more resistance. 2. Cross-sectional area (A): R ∝ 1/A — thicker wire has less resistance. 3. Material (resistivity ρ): R = ρL/A. 4. Temperature: Resistance of metals increases with temperature.
Series and Parallel Circuits — Full Derivations
Series Circuit
In a series circuit, the same current flows through every component. The total voltage is split across the components.
Derivation of total resistance:
Key facts — Series:
- Current: same through all (I₁ = I₂ = I₃ = I)
- Voltage: divides (V = V₁ + V₂ + V₃)
- Total resistance: greater than any individual resistance
- Failure: if one component breaks, the whole circuit stops (like old Christmas lights)
Parallel Circuit
In a parallel circuit, the same voltage is applied across every branch. The total current splits across the branches.
Derivation of total resistance:
Key facts — Parallel:
- Voltage: same across all branches (V₁ = V₂ = V₃ = V)
- Current: divides (I = I₁ + I₂ + I₃)
- Total resistance: less than the smallest individual resistance
- Failure: if one branch breaks, other branches continue working (household wiring is parallel)
Series vs Parallel — Comparison Table
| Property | Series | Parallel |
|---|---|---|
| Current | Same through all | Splits across branches |
| Voltage | Splits across components | Same across all branches |
| Total resistance | R₁ + R₂ + R₃ (increases) | Less than smallest R (decreases) |
| Effect of one failure | Entire circuit breaks | Other branches still work |
| Use | Decorative string lights | Household appliances |
Joule's Heating Effect
When current flows through a resistor, electrical energy is converted to heat.
Where H = heat produced (J), I = current (A), R = resistance (Ω), t = time (s).
Why I² and not just I? Because both the voltage drop (V = IR) and the current (I) increase with I, so power P = VI = I²R, and heat = power × time.
Applications:
and breaks the circuit, protecting appliances.
- Electric iron, heater, toaster: Deliberately use high-resistance wire (nichrome) to produce heat.
- Electric fuse / MCB: When current exceeds safe limit, the fuse wire melts (due to I²Rt heating)
- Incandescent bulb: Tungsten filament heats to ~2500°C and glows — heat produces light.
Worked Numerical Examples
Example 1 — Basic Ohm's Law
Problem: A resistor of 4 Ω is connected to a 12 V battery. Find the current.
Example 2 — Series Circuit
Problem: Two resistors of 6 Ω and 3 Ω are connected in series to an 18 V battery. Find the total resistance and the current.
Example 3 — Parallel Circuit
Problem: Two resistors of 6 Ω and 3 Ω are connected in parallel. Find the equivalent resistance.
Example 4 — Electrical Energy (Units Consumed)
Problem: A 60 W bulb is used for 5 hours daily for 30 days. Find the electrical energy consumed in kilowatt-hours (units).
Example 5 — Wire Stretched to Double Length
Problem: A wire has resistance 8 Ω. It is stretched to double its original length. Find the new resistance.
Example 6 — Power and Current from Voltage and Resistance
Problem: An electric iron has a resistance of 44 Ω and is connected to a 220 V supply. Find the current drawn and the power consumed.
Board Exam Q&A — Model Answers
One Mark Questions
Q: What is electric current? Write its SI unit. A: Electric current is the rate of flow of electric charge through a conductor. I = Q/t. SI unit: ampere (A). 1 A = 1 coulomb per second.
Q: Define 1 ohm of resistance. A: The resistance of a conductor is 1 ohm if a potential difference of 1 volt causes a current of 1 ampere to flow through it. (1 Ω = 1 V/A)
Q: What is 1 kilowatt-hour? A: 1 kilowatt-hour (kWh) is the amount of electrical energy consumed by a device of power 1 kW working for 1 hour. It is the commercial unit of electrical energy, called 1 unit on the bill.
Q: State Ohm's law. A: At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends. V = IR.
Two Mark Questions
Q: Differentiate between series and parallel circuits.
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same through all components | Divides across branches |
| Voltage | Divides across components | Same across all branches |
| Total resistance | Sum of all resistances (increases) | Less than smallest resistance (decreases) |
Q: Why are household appliances connected in parallel and not in series? A: In a parallel circuit, each appliance gets the full supply voltage (220 V), allowing it to work at its rated power. Also, each appliance can be switched on/off independently without affecting others. In a series circuit, the voltage is shared, appliances get less than rated voltage, and if one breaks, all stop working.
Q: What is Joule's heating effect? Write its formula. A: When electric current flows through a resistor, the electrical energy is converted to heat energy. This is called Joule's heating effect. Formula: H = I²Rt, where H is the heat produced (joules), I is current (A), R is resistance (Ω), and t is time (s).
Five Mark Questions
Q: Derive the equivalent resistance of resistors connected (a) in series and (b) in parallel.
(a) Series: In series, the same current I flows through all resistors. The total voltage V = V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃ = I(R₁ + R₂ + R₃). Since V = I × R_total: R_total = R₁ + R₂ + R₃
(b) Parallel: In parallel, the same voltage V is applied across all resistors. Total current I = I₁ + I₂ + I₃ = V/R₁ + V/R₂ + V/R₃ = V(1/R₁ + 1/R₂ + 1/R₃). Since I = V/R_total: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
Q: Explain Joule's law of heating. Derive the formula and give two practical applications.
When a current I flows through a resistance R for time t, work is done by the electric field on the charges. This work appears as heat in the conductor.
Derivation:
So H = I²Rt (Joule's law of heating).
Applications: 1. Electric heater / iron / toaster: Uses nichrome wire (high resistance) so that I²Rt produces large amounts of heat deliberately. 2. Electric fuse: A thin wire with low melting point. When current exceeds safe value, I²Rt heating melts the wire and breaks the circuit, protecting appliances.
Common Board Exam Mistakes
whichever matches the given quantities.
at the end to get R_total.
- Confusing current and voltage: Current (I) is what flows; voltage (V) is the push.
- Forgetting household circuits are parallel: Always state this when asked about household wiring.
- Missing units in numerical answers: Write A, V, Ω, W, or J with every answer.
- Using the wrong power formula: P = VI, P = I²R, and P = V²/R are all equivalent — use
- Parallel resistance error: Students often add 1/R values but forget to take the reciprocal
Tamil Nadu Board Exam Pattern
OR Joule's heating law derivation) — this is almost certain every year.
- Chapter weightage: 7–10 marks (the highest-scoring single chapter in science)
- Five-mark questions: Usually 1 five-mark derivation (series/parallel equivalent resistance
- Numericals: Expect 1–2 numerical problems — practice all six examples above.
- Definitions: At least 2 one-mark and 1 two-mark definition question.
- Tip: If the 5-mark asks for "derive AND give applications", do both — don't skip applications.
Revision Checklist
- Ohm's law stated and V = IR written from memory
- Series derivation: R_total = R₁ + R₂ + R₃ with reasoning
- Parallel derivation: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ with reasoning
- Joule's heating H = I²Rt — formula and two applications
- Series vs parallel comparison table memorised
- All six worked numericals solved independently
- Power formula variants: P = VI = I²R = V²/R — all three memorised