CBSE Class 10 Electricity — Complete Chapter Guide with Solved Numericals

In short: Electricity is the highest-scoring Physics chapter in CBSE Class 10, carrying 8-9 marks. This chapter is numerical-heavy — master Ohm's Law (V = IR), resistance combinations (series and parallel), electrical power (P = VI = I²R = V²/R), and Joule's heating formula (H = I²Rt). Five well-practiced numerical types cover almost every possible board question.

Electricity is the chapter where marks come from practice, not memorization. Unlike Biology chapters where you write paragraphs, here you solve numericals — and the question patterns repeat year after year. If you can confidently solve problems on Ohm's Law, series-parallel circuits, and power calculations, you are looking at 8-9 marks almost guaranteed.

This guide walks through every concept with formulas, circuit tips, and 5 solved numericals that cover every board exam pattern. For the marks distribution across all Science chapters, check the CBSE Class 10 Science chapter-wise marks weightage.

Electric Current and Circuit Basics

Electric current is the rate of flow of electric charge through a conductor. If a charge Q flows through a conductor in time t:

I = Q/t

Where I is current in amperes (A), Q is charge in coulombs (C), and t is time in seconds (s). One ampere means one coulomb of charge flowing per second.

Conventional current flows from the positive terminal to the negative terminal of a battery (opposite to the actual electron flow).

A complete electric circuit needs: a source of potential difference (battery/cell), a conductor (wire), and optionally a load (resistor, bulb) and a switch. If the circuit is broken at any point, current stops flowing — this is an open circuit.

Ohm's Law

Ohm's Law states that the potential difference (V) across the ends of a conductor is directly proportional to the current (I) flowing through it, provided the temperature remains constant.

V = IR

Where R is the resistance of the conductor, measured in ohms (Ω).

This can be rearranged as:

• I = V/R (to find current)
• R = V/I (to find resistance)

V-I Graph: For an ohmic conductor (one that follows Ohm's law), the V-I graph is a straight line passing through the origin. The slope of this line gives the resistance.

Resistance and Factors Affecting It

Resistance is the opposition to the flow of current. The resistance of a conductor depends on:

1. Length (L): R is directly proportional to L. Longer wire = more resistance.
2. Cross-sectional area (A): R is inversely proportional to A. Thicker wire = less resistance.
3. Material: Different materials have different resistivities.
4. Temperature: Resistance of metals increases with temperature.

The formula combining these factors:

R = ρL/A

Where ρ (rho) is the resistivity of the material, measured in Ω·m (ohm-metre).

Resistivity values of common materials:

Board Exam Tip: "Why is nichrome used in heating elements?" and "Why is copper used in wiring?" are frequently asked 1-2 mark questions. The answer always connects back to resistivity.

Resistors in Series

When resistors are connected end to end (one after another), they are in series.

Equivalent resistance: R = R1 + R2 + R3

Key properties of series combination:

• The current through each resistor is the same (I is constant).
• The total voltage is the sum of voltages across each resistor: V = V1 + V2 + V3.
• The equivalent resistance is always greater than the largest individual resistance.
• If one component fails, the entire circuit breaks.

When to use: Series combination is used in decorative light strings and voltage dividers.

Resistors in Parallel

When resistors are connected between the same two points, they are in parallel.

Equivalent resistance: 1/R = 1/R1 + 1/R2 + 1/R3

Key properties of parallel combination:

• The voltage across each resistor is the same (V is constant).
• The total current is the sum of currents through each resistor: I = I1 + I2 + I3.
• The equivalent resistance is always less than the smallest individual resistance.
• If one component fails, others continue to work.

When to use: Household appliances are connected in parallel so that each gets the full voltage and can be operated independently.

Quick formula for two resistors in parallel:

R = (R1 × R2) / (R1 + R2)

This shortcut saves time in board exams.

Comparison: Series vs Parallel

Electrical Power and Energy

Power is the rate of doing electrical work or the rate of consuming electrical energy.

P = VI

Using Ohm's Law, this can be written in three forms:

• P = VI (when V and I are known)
• P = I²R (when I and R are known)
• P = V²/R (when V and R are known)

The SI unit of power is watt (W). 1 watt = 1 volt × 1 ampere.

Electrical energy consumed is:

E = P × t = VIt

The commercial unit of energy is the kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ joules. This is what your electricity bill is based on.

Calculating electricity bill: Energy consumed (in kWh) = Power (in kW) × Time (in hours) Cost = Energy (kWh) × Rate per unit

Heating Effect of Electric Current — Joule's Law

When current flows through a resistor, electrical energy is converted to heat. This is the heating effect of current.

Joule's law of heating:

H = I²Rt

Where H is heat produced in joules, I is current in amperes, R is resistance in ohms, and t is time in seconds.

Applications: Electric heater, electric iron, electric toaster, fuse wire, electric bulb.

Fuse wire: A thin wire of low melting point (alloy of lead and tin) placed in series with the circuit. When current exceeds the rated value, the fuse melts and breaks the circuit, protecting appliances.

Circuit Diagram Drawing Tips

Board exams often ask you to draw circuit diagrams. Use standard symbols:

• Cell: two parallel lines (longer line is positive terminal)
• Battery: multiple cells in series
• Resistor: zigzag line or rectangular box
• Ammeter: circle with A (always connected in series)
• Voltmeter: circle with V (always connected in parallel)
• Switch: break in the line with a small lever

Keep lines straight. Use a ruler. Label all components and their values. A clean diagram earns full marks.

Solved Numericals

Numerical 1: Ohm's Law

A potential difference of 12 V is applied across a resistance of 4 Ω. Find the current flowing through the resistor.

Using V = IR: 12 = I × 4 I = 12/4 = 3 A

The current flowing is 3 amperes.

Numerical 2: Series Combination

Three resistors of 5 Ω, 10 Ω, and 15 Ω are connected in series to a 30 V battery. Find the equivalent resistance and the current in the circuit.

Equivalent resistance: R = 5 + 10 + 15 = 30 Ω Current: I = V/R = 30/30 = 1 A

Voltage across each resistor: V1 = IR1 = 1 × 5 = 5 V V2 = IR2 = 1 × 10 = 10 V V3 = IR3 = 1 × 15 = 15 V

Verification: V1 + V2 + V3 = 5 + 10 + 15 = 30 V = Total voltage. Correct.

Numerical 3: Parallel Combination

Two resistors of 6 Ω and 12 Ω are connected in parallel across a 12 V battery. Find the equivalent resistance, total current, and current through each resistor.

Equivalent resistance: 1/R = 1/6 + 1/12 = (2 + 1)/12 = 3/12 = 1/4 R = 4 Ω

Total current: I = V/R = 12/4 = 3 A

Current through 6 Ω: I1 = V/R1 = 12/6 = 2 A Current through 12 Ω: I2 = V/R2 = 12/12 = 1 A

Verification: I1 + I2 = 2 + 1 = 3 A = Total current. Correct.

Numerical 4: Power and Energy

An electric heater of resistance 20 Ω draws a current of 5 A. Find the power consumed and the heat generated in 30 minutes.

Power: P = I²R = (5)² × 20 = 25 × 20 = 500 W

Time = 30 minutes = 30 × 60 = 1800 seconds

Heat generated: H = I²Rt = 25 × 20 × 1800 = 9,00,000 J = 900 kJ

Alternatively: H = P × t = 500 × 1800 = 9,00,000 J

In kWh: Energy = 0.5 kW × 0.5 hours = 0.25 kWh

Numerical 5: Mixed Circuit

Two resistors of 4 Ω each are connected in parallel, and this combination is connected in series with a 2 Ω resistor. The circuit is connected to a 12 V battery. Find the total current and the power consumed.

Step 1: Find equivalent of parallel combination. 1/Rp = 1/4 + 1/4 = 2/4 = 1/2 Rp = 2 Ω

Step 2: Total resistance (series with 2 Ω). R = Rp + 2 = 2 + 2 = 4 Ω

Step 3: Total current. I = V/R = 12/4 = 3 A

Step 4: Power consumed. P = V²/R = 144/4 = 36 W

Or P = VI = 12 × 3 = 36 W

Common Board Exam Mistakes

1. Not simplifying mixed circuits step by step. Always identify parallel groups first, find their equivalent, then treat the result as a series circuit.
2. Confusing ammeter and voltmeter connections. Ammeter is always in series (low resistance), voltmeter is always in parallel (high resistance).
3. Using wrong power formula. When V and R are given, use P = V²/R. When I and R are given, use P = I²R. Choosing the wrong form leads to extra steps and errors.
4. Forgetting unit conversions. Convert minutes to seconds for Joule's law. Convert watts to kilowatts and hours for energy bills.
5. Not verifying answers. After finding individual voltages in series or currents in parallel, check that they add up to the total.

Board Exam Important Question Types

• One numerical on series or parallel combination (3 marks) — almost guaranteed every year.
• One numerical on power, energy, or heating effect (3 marks).
• "Why are household appliances connected in parallel?" (2 marks).
• "What is the function of a fuse?" (1-2 marks).
• MCQs on Ohm's law graph, resistance formula, and unit conversions.

For the full formula list, refer to the CBSE Class 10 Science formulas complete list.

Frequently Asked Questions

How many marks does Electricity carry in CBSE Class 10?

Electricity typically carries 8 to 9 marks in the board exam, making it the highest-scoring Physics chapter. You can expect at least two 3-mark numericals and one or two 1-2 mark conceptual questions. Since the question patterns repeat, thorough practice of standard numericals can guarantee nearly full marks.

What is the difference between series and parallel circuits?

In a series circuit, components are connected end-to-end, so current is the same through all but voltage divides. In a parallel circuit, components are connected between the same two points, so voltage is the same across all but current divides. Household appliances use parallel connections so each device gets full voltage and operates independently.

How do I solve mixed circuit problems?

Break the problem into steps. First, identify which resistors are in parallel and calculate their equivalent resistance. Then treat that equivalent as a single resistor in series with the remaining resistors. Calculate total resistance, then find current using V = IR. Work backward to find individual voltages and currents. Always verify by checking that partial values add up to totals.

What is the difference between kWh and joule?

Both are units of energy. The joule (J) is the SI unit, while the kilowatt-hour (kWh) is the commercial unit used in electricity bills. 1 kWh = 3.6 × 10⁶ joules. To convert, use: Energy (kWh) = Power (kW) × Time (hours). Your electricity meter measures consumption in kWh, commonly called "units."

Why is Joule's law important for board exams?

Joule's law (H = I²Rt) explains the heating effect of current and is the basis for questions on electric heaters, fuses, and electric bulbs. Board exams frequently ask numericals where you calculate heat generated by a device over a given time. It also connects to practical applications like why fuse wires melt (high current, low melting point) and why heating elements use nichrome (high resistivity).

How can I draw neat circuit diagrams in the exam?

Use a ruler for all straight lines. Draw standard symbols (zigzag for resistor, circle with A for ammeter, circle with V for voltmeter). Keep the circuit rectangular with components on the sides. Label all values (resistance, voltage, current). Connect the ammeter in series and voltmeter in parallel. A clean, labeled diagram with correct connections earns full marks even before you start calculations.

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