Electricity Chapter (Class 10): Complete Notes with Solved Numericals
Tushar Parik
Author
Electricity Made Simple — From Ohm's Law to Solved Board Numericals
The Electricity chapter is the highest-scoring numerical-based topic in Class 10 Physics for both CBSE and ICSE boards. It carries 15-20 marks in the theory paper and rewards students who practise systematically. This guide covers every concept you need — Ohm's law, resistance and resistivity, series and parallel circuits, Kirchhoff's laws, electrical power and energy — with step-by-step solved numericals, circuit diagram tips, and the exact question types board examiners repeat year after year. Whether you are revising for the first time or doing a final brush-up, this is your one-stop resource.
In This Article
- Electric Current, Potential Difference & Circuit Basics
- Ohm's Law — Statement, Formula & V-I Graph
- Resistance, Resistivity & Factors Affecting Resistance
- Series & Parallel Circuits — Formulas & Comparison
- Kirchhoff's Laws — Junction & Loop Rules
- Electrical Power & Energy — Formulas & Applications
- Solved Numericals — Step-by-Step Board-Style Problems
- Circuit Diagram Tips for Board Exams
- Most Repeated Exam Questions
- Frequently Asked Questions
Electric Current, Potential Difference & Circuit Basics
Before diving into formulas, make sure these foundational concepts are rock solid. Every numerical in this chapter builds on them.
- Electric Current (I): The rate of flow of electric charge through a conductor. Formula: I = Q/t, where Q is charge in coulombs (C) and t is time in seconds (s). SI unit: ampere (A). One ampere means one coulomb of charge flows per second.
- Potential Difference (V): The work done per unit charge to move a charge between two points. Formula: V = W/Q, where W is work done in joules (J). SI unit: volt (V). One volt means one joule of work is done to move one coulomb of charge.
- Direction of Current: Conventional current flows from the positive terminal to the negative terminal of a cell (opposite to electron flow). Always mark this direction on circuit diagrams.
- Circuit Components: A closed circuit requires a source of EMF (cell/battery), conducting wires, a load (resistor/bulb), and a switch. An ammeter is connected in series to measure current; a voltmeter is connected in parallel to measure potential difference.
Ohm's Law — Statement, Formula & V-I Graph
Ohm's Law is the single most important relationship in this chapter. It connects voltage, current, and resistance and is the starting point for nearly every numerical you will encounter in the board exam.
Statement
At constant temperature, the electric current flowing through a metallic conductor is directly proportional to the potential difference applied across its ends.
Mathematical Form
V = IR, where V = potential difference (volts), I = current (amperes), R = resistance (ohms, Ω).
Derived Forms
- I = V/R (to find current when voltage and resistance are known)
- R = V/I (to find resistance from voltage and current measurements)
V-I Graph: When you plot potential difference (V) on the y-axis against current (I) on the x-axis, a conductor obeying Ohm's law gives a straight line passing through the origin. The slope of this line equals the resistance (R = V/I). A steeper slope means higher resistance. This graph is frequently asked in board exams — practise drawing it with properly labelled axes.
Exam Tip
Ohm's Law is valid only at constant temperature. The moment temperature changes, resistance changes (for metals, resistance increases with temperature). If a question says "assuming constant temperature" or "at a given temperature," it is signalling you to apply Ohm's Law directly.
Resistance, Resistivity & Factors Affecting Resistance
Resistance is the property of a conductor that opposes the flow of electric current. Understanding what affects resistance is crucial for both theory and numericals.
Formula for Resistance
R = ρL/A, where ρ (rho) = resistivity of the material (Ω·m), L = length of the conductor (m), A = cross-sectional area (m²).
Four Factors Affecting Resistance
- Length (L): R is directly proportional to L. Doubling the length doubles the resistance.
- Cross-sectional Area (A): R is inversely proportional to A. A thicker wire has lower resistance.
- Material (ρ): Different materials have different resistivities. Copper (ρ ≈ 1.7 × 10⁻&sup8; Ω·m) has much lower resistivity than nichrome (ρ ≈ 1.0 × 10⁻&sup6; Ω·m).
- Temperature: For metallic conductors, resistance increases with temperature. For semiconductors, resistance decreases with temperature.
| Material | Resistivity (Ω·m) | Common Use |
|---|---|---|
| Silver | 1.6 × 10⁻&sup8; | Best conductor (expensive, limited use) |
| Copper | 1.7 × 10⁻&sup8; | Electrical wiring, cables |
| Aluminium | 2.6 × 10⁻&sup8; | Overhead power lines (lighter than copper) |
| Nichrome | 1.0 × 10⁻&sup6; | Heating elements (high resistance) |
| Rubber | 10¹³ to 10¹&sup6; | Insulation (extremely high resistance) |
Series & Parallel Circuits — Formulas & Comparison
Combination circuits are the most frequently tested topic in the Electricity chapter. Board exams consistently include a 5-6 mark numerical involving resistors in series and parallel. Master both configurations and their properties.
Resistors in Series
- Total Resistance: Rtotal = R1 + R2 + R3 + ... (resistance increases)
- Current: Same through all resistors (I1 = I2 = I3 = I)
- Voltage: Divides across resistors (V = V1 + V2 + V3)
- Key property: The total resistance is always greater than the largest individual resistance.
- If one component fails: The entire circuit breaks (current stops flowing).
Resistors in Parallel
- Total Resistance: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... (resistance decreases)
- For two resistors: Rtotal = (R1 × R2) / (R1 + R2) — this shortcut saves time in exams.
- Current: Divides across branches (I = I1 + I2 + I3)
- Voltage: Same across all resistors (V1 = V2 = V3 = V)
- Key property: The total resistance is always less than the smallest individual resistance.
- If one component fails: Other branches continue working. This is why household appliances are connected in parallel.
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same through all components | Divides among branches |
| Voltage | Divides across components | Same across all branches |
| Total Resistance | R = R1 + R2 + R3 | 1/R = 1/R1 + 1/R2 + 1/R3 |
| Effect of Adding Resistors | Total resistance increases | Total resistance decreases |
| Household Use | Decorative lights (fairy lights) | All household appliances |
Kirchhoff's Laws — Junction & Loop Rules
Kirchhoff's laws extend Ohm's law to complex circuits with multiple loops and junctions. While CBSE Class 10 introduces these conceptually, ICSE students and those preparing for competitive exams need to apply them in numericals. Understanding these laws gives you the tools to solve any circuit problem.
Kirchhoff's First Law (Junction Rule / Current Law)
The algebraic sum of currents meeting at any junction (node) in a circuit is zero. In simpler terms: the total current entering a junction equals the total current leaving it.
Formula: ΣIin = ΣIout. This law is based on the conservation of electric charge — charge cannot accumulate at a junction.
Kirchhoff's Second Law (Loop Rule / Voltage Law)
The algebraic sum of all potential differences (voltages) around any closed loop in a circuit is zero. In simpler terms: the sum of EMFs equals the sum of voltage drops across resistances in a closed loop.
Formula: ΣV = 0 around any closed loop. This law is based on the conservation of energy — a charge gains as much energy from EMF sources as it loses across resistances in one complete loop.
How to Apply Kirchhoff's Laws (Step-by-Step)
- Label all currents in each branch with assumed directions (I1, I2, I3, etc.).
- Apply the junction rule at each node to write current equations.
- Choose independent loops and traverse each loop in one direction (clockwise or anticlockwise).
- For each loop, write the voltage equation: EMF rises are positive, EMF drops are negative; IR drops follow the sign convention based on your traversal direction.
- Solve the simultaneous equations to find unknown currents. If a current comes out negative, it simply means the actual direction is opposite to your assumed direction.
Electrical Power & Energy — Formulas & Applications
Electrical power and energy questions appear in both CBSE and ICSE board exams every year. They test your ability to apply multiple formulas and convert between units, especially the kilowatt-hour (kWh) used in electricity bills.
Power Formulas
- P = VI — Power = Voltage × Current (fundamental formula)
- P = I²R — Derived by substituting V = IR (useful when current and resistance are known)
- P = V²/R — Derived by substituting I = V/R (useful when voltage and resistance are known)
- SI Unit: Watt (W). 1 watt = 1 joule per second = 1 volt × 1 ampere.
- Larger unit: Kilowatt (kW). 1 kW = 1000 W.
Energy Formulas
- E = Pt — Energy = Power × Time
- E = VIt — Energy = Voltage × Current × Time
- E = I²Rt — Joule's law of heating (heat produced in a resistor)
- E = V²t/R — Energy when voltage and resistance are known
- SI Unit: Joule (J). 1 J = 1 W × 1 s.
- Commercial Unit: Kilowatt-hour (kWh). 1 kWh = 3.6 × 10&sup6; J = 1 unit of electricity.
Electricity Bill Calculation
Cost = Energy consumed (in kWh) × Rate per unit. To calculate energy in kWh: convert power to kW (divide watts by 1000), multiply by time in hours. Example: A 100 W bulb used for 10 hours per day for 30 days consumes (100/1000) × 10 × 30 = 30 kWh = 30 units.
Solved Numericals — Step-by-Step Board-Style Problems
These are the exact types of numericals that appear in CBSE and ICSE board exams. Follow the Given → To Find → Formula → Solution → Answer protocol for full marks.
Numerical 1: Ohm's Law
Problem:
A wire of resistance 20 Ω is connected to a 12 V battery. Find the current flowing through the wire.
Solution:
Given: R = 20 Ω, V = 12 V
To find: I = ?
Using Ohm's Law: V = IR
I = V/R = 12/20 = 0.6 A
Answer: The current flowing through the wire is 0.6 A.
Numerical 2: Resistors in Series
Problem:
Three resistors of 5 Ω, 10 Ω, and 15 Ω are connected in series across a 30 V battery. Find: (a) the total resistance, (b) the current in the circuit, (c) the voltage across each resistor.
Solution:
(a) Rtotal = R1 + R2 + R3 = 5 + 10 + 15 = 30 Ω
(b) I = V/Rtotal = 30/30 = 1 A
(c) 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 = V (verified)
Answer: Rtotal = 30 Ω, I = 1 A, V1 = 5 V, V2 = 10 V, V3 = 15 V.
Numerical 3: Resistors in Parallel
Problem:
Two resistors of 6 Ω and 12 Ω are connected in parallel across a 24 V supply. Find: (a) the equivalent resistance, (b) the total current, (c) the current through each resistor.
Solution:
(a) 1/Req = 1/R1 + 1/R2 = 1/6 + 1/12 = (2 + 1)/12 = 3/12 = 1/4
Req = 4 Ω
(b) Itotal = V/Req = 24/4 = 6 A
(c) I1 = V/R1 = 24/6 = 4 A
I2 = V/R2 = 24/12 = 2 A
Verification: I1 + I2 = 4 + 2 = 6 A = Itotal (verified)
Answer: Req = 4 Ω, Itotal = 6 A, I1 = 4 A, I2 = 2 A.
Numerical 4: Combination Circuit (Series + Parallel)
Problem:
A 4 Ω resistor is connected in series with a parallel combination of 6 Ω and 12 Ω resistors. The circuit is connected to a 24 V battery. Find the total resistance, total current, and power consumed by the circuit.
Solution:
Step 1: Find the equivalent resistance of the parallel combination.
1/Rp = 1/6 + 1/12 = (2 + 1)/12 = 3/12 = 1/4
Rp = 4 Ω
Step 2: Find the total resistance (series combination of 4 Ω and Rp).
Rtotal = 4 + 4 = 8 Ω
Step 3: Find the total current.
I = V/Rtotal = 24/8 = 3 A
Step 4: Find the power consumed.
P = VI = 24 × 3 = 72 W
Answer: Rtotal = 8 Ω, I = 3 A, P = 72 W.
Numerical 5: Electrical Energy & Cost
Problem:
An electric heater rated 1000 W is used for 2 hours daily for 30 days. If the cost of electricity is &rupee;5 per unit, find the total cost of running the heater.
Solution:
Power = 1000 W = 1 kW
Time per day = 2 hours
Total time = 2 × 30 = 60 hours
Energy consumed = P × t = 1 kW × 60 h = 60 kWh = 60 units
Total cost = 60 × 5 = &rupee;300
Answer: Total energy consumed = 60 kWh. Total cost = &rupee;300.
Numerical 6: Resistivity
Problem:
A copper wire of length 2 m and cross-sectional area 1.0 × 10⁻&sup6; m² has a resistivity of 1.7 × 10⁻&sup8; Ω·m. Find its resistance. If a potential difference of 3.4 V is applied across it, find the current.
Solution:
R = ρL/A = (1.7 × 10⁻&sup8; × 2) / (1.0 × 10⁻&sup6;)
R = 3.4 × 10⁻&sup8; / 1.0 × 10⁻&sup6; = 0.034 Ω
I = V/R = 3.4 / 0.034 = 100 A
Answer: R = 0.034 Ω, I = 100 A.
Circuit Diagram Tips for Board Exams
Neat, properly labelled circuit diagrams carry 2-3 marks and are among the easiest marks on the paper. Follow these rules and you will never lose marks on diagram-based questions.
1. Use Standard Symbols
Never draw realistic pictures of batteries or bulbs. Use the standard circuit symbols: two lines for a cell (longer line = positive), a zigzag or rectangle for a resistor, A inside a circle for an ammeter, V inside a circle for a voltmeter.
2. Use a Ruler for All Straight Lines
Draw all connecting wires as straight horizontal or vertical lines. Use right-angle turns at junctions. Freehand circuit diagrams look messy and lose presentation marks.
3. Mark Current Direction
Always draw arrows showing the direction of conventional current (from positive to negative terminal of the battery). This helps you identify series and parallel connections and is required for full marks.
4. Label Every Component
Write resistance values (e.g., 5 Ω, 10 Ω), voltage across cells, and ammeter/voltmeter readings. An unlabelled diagram loses marks even if it is otherwise correct. Include + and − signs on the battery.
5. Ammeter in Series, Voltmeter in Parallel
This is the most common mistake students make. An ammeter has very low resistance and must be connected in series. A voltmeter has very high resistance and must be connected in parallel across the component being measured.
6. Redraw Combination Circuits
Before solving any combination circuit numerical, redraw the circuit clearly showing which resistors are in series and which are in parallel. This single step prevents most calculation errors and shows the examiner your approach.
Most Repeated Exam Questions
Based on analysis of CBSE and ICSE board papers (2018–2025), these question types appear most frequently. Prepare all of them for guaranteed marks.
- State Ohm's law. Draw the V-I graph for an ohmic conductor. (2-3 marks — appears nearly every year)
- Derive the expression for equivalent resistance of resistors in series/parallel. (3-5 marks — a board exam staple)
- Combination circuit numerical: Given a circuit with resistors in series and parallel, find total resistance, current, and voltage across each resistor. (5-6 marks)
- Electrical energy and cost: Calculate the energy consumed by an appliance over a period and find the electricity bill. (3-4 marks)
- Factors affecting resistance: How does resistance change when length is doubled, area is halved, etc. (2-3 marks)
- Draw a circuit diagram showing an ammeter and voltmeter connected to verify Ohm's law. (2-3 marks)
- Why are household appliances connected in parallel? Give three reasons. (2-3 marks)
- Heating effect of current: Derive H = I²Rt and explain its applications (electric heater, fuse, electric iron). (3-5 marks)
- Define the kilowatt-hour. Express it in joules. (1-2 marks)
- Resistivity numerical: Calculate resistance from given length, area, and resistivity. (2-3 marks)
Frequently Asked Questions
Q: How many marks does the Electricity chapter carry in the Class 10 board exam?
In the CBSE Class 10 Science paper, Electricity carries approximately 10-12 marks out of 80. In the ICSE Physics paper, Current Electricity carries 15-16 marks out of 80 (roughly 20% of the theory paper). In both boards, it is one of the two highest-scoring chapters alongside Light/Optics. Numericals from this chapter can appear as both short-answer (2-3 marks) and long-answer (5-6 marks) questions.
Q: What are the most important formulas to memorise for the Electricity chapter?
The six essential formulas are: (1) Ohm's law: V = IR, (2) Resistance: R = ρL/A, (3) Series resistance: R = R1 + R2 + R3, (4) Parallel resistance: 1/R = 1/R1 + 1/R2 + 1/R3, (5) Power: P = VI = I²R = V²/R, (6) Energy: E = Pt = VIt = I²Rt. Write these six formulas on a card and revise them daily. Every numerical in this chapter can be solved using one or a combination of these formulas.
Q: What is the difference between resistance and resistivity?
Resistance (R) is the opposition to current flow offered by a specific conductor and depends on its length, area, material, and temperature. It is measured in ohms (Ω). Resistivity (ρ) is a property of the material itself and does not depend on the dimensions of the conductor. It is measured in ohm-metre (Ω·m). Two copper wires of different lengths will have different resistances but the same resistivity. Resistivity helps compare materials: copper has low resistivity (good conductor), nichrome has high resistivity (used in heating elements).
Q: Why are household appliances connected in parallel and not in series?
There are three key reasons. First, each appliance receives the full mains voltage (220 V in India) because voltage is the same across all parallel branches. In series, the voltage would divide and no appliance would work at its rated capacity. Second, if one appliance fails, the others continue to work because each branch is independent. In series, one failure breaks the entire circuit. Third, each appliance can be switched on or off independently using its own switch. This question is asked repeatedly in board exams — memorise all three reasons.
Q: How should I approach combination circuit numericals in the exam?
Follow this five-step method: (1) Identify which resistors are in series and which are in parallel by tracing the current path, (2) Redraw the circuit if it looks complicated — simplify it step by step, (3) Calculate the equivalent resistance of the parallel combination first, (4) Add it to the series resistors to get the total resistance, (5) Use V = IR to find current, then work backwards to find voltage and current through each resistor. Always verify your answer: the sum of voltages across components in series should equal the battery voltage, and the sum of currents through parallel branches should equal the total current.
Q: Is Kirchhoff's law included in the Class 10 CBSE syllabus?
Kirchhoff's laws are not explicitly part of the standard CBSE Class 10 syllabus but are introduced conceptually through series and parallel circuit analysis. The junction rule (current conservation) is implicitly used whenever you write I = I1 + I2 for parallel circuits, and the loop rule (voltage conservation) is used when you write V = V1 + V2 for series circuits. For ICSE students, a basic understanding of Kirchhoff's laws is beneficial as it appears in some reference books and helps solve complex circuit problems. Students preparing for competitive exams like NTSE or Olympiads should study Kirchhoff's laws in detail.
Q: What common mistakes should I avoid in Electricity numericals?
The five most common errors are: (1) Confusing the series and parallel formulas — remember, in series you add resistances directly, in parallel you add their reciprocals, (2) Forgetting to convert units — power from watts to kilowatts for kWh calculations, time from minutes to hours or seconds, (3) Not writing units in the final answer — examiners deduct marks for missing units, (4) Incorrect ammeter/voltmeter placement in circuit diagrams — ammeter in series, voltmeter in parallel, and (5) Arithmetic errors in fraction calculations for parallel resistance — always double-check your LCM. Using the verification step (total voltage check, total current check) catches most of these mistakes.
Q: How many numericals should I practise from this chapter before the board exam?
Aim for at least 40-50 numericals spread across all types: 8-10 on Ohm's law, 10-12 on series and parallel combinations, 5-6 on combination circuits (mixed series-parallel), 5-6 on electrical power and energy, 3-4 on resistivity, and 3-4 on electricity bill calculations. Solve all NCERT textbook examples and exercise problems first, then move to previous year board papers. After 50 problems, you will find that every new question is just a variation of a pattern you have already seen. The key is not just solving them but following the step-by-step protocol every single time so it becomes automatic in the exam.
Electricity Is a Guaranteed Scoring Chapter — If You Practise Right
Unlike chapters that require lengthy theoretical answers, Electricity rewards precision and practice. Master the six core formulas, solve at least 50 numericals, draw clean circuit diagrams with a ruler, and you will walk into the exam hall knowing that 15-20 marks are already secured. Use this guide as your complete revision companion — every concept, formula, and solved problem you need is right here.
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