Class 10 Science Chapter 11 Electricity — Formulas & Key Points

This master table lists every mathematical relationship you need from NCERT Class 10 Science Chapter 11. Commit these to memory and practise identifying which formula applies to each problem type. Many students lose marks not because they cannot solve, but because they pick the wrong formula. Pay special attention to the 'When to Use' column — it tells you the exact scenario where each formula is valid. For example, Ohm's law V = IR is valid only for ohmic conductors (those that obey a linear V-I relationship) at constant temperature. Applying it blindly to diodes or thermistors will give wrong answers. Similarly, the heating effect formula H = I²Rt is the most versatile form because current is common in series circuits, while H = V²t/R works better when voltage is constant across parallel branches.

Ohm's law is the foundation of this chapter. It states that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, provided temperature and other physical conditions remain constant. Mathematically, V = IR, where R is the resistance in ohms (Ω). Not all materials obey Ohm's law; those that do are called ohmic conductors (example: metallic wires at constant temperature). Non-ohmic examples include diodes, LEDs and filament lamps. Resistance is the property of a conductor that opposes the flow of electric current. It depends on the material, length, cross-sectional area and temperature of the conductor. The SI unit is the ohm (Ω). A higher resistance means less current for the same voltage.

Resistivity (ρ, Greek letter rho) is an intrinsic property of a material that quantifies how strongly it resists current flow, independent of its shape or size. The formula linking resistance R, resistivity ρ, length L and cross-sectional area A is R = ρ L / A. Rearranging, ρ = R A / L. The SI unit of resistivity is ohm-metre (Ω·m). Good conductors like copper and silver have very low resistivity (around 10⁻⁸ Ω·m), while insulators like rubber have resistivity above 10¹³ Ω·m. Resistivity increases with temperature for conductors and generally decreases for semiconductors. NCERT Class 10 Science gives a table of resistivities for common materials; memorise approximate values for copper, nichrome and glass for quick MCQ answering.

When resistors are connected in series, the same current flows through each resistor, but the voltage divides. The total or equivalent resistance R_s = R₁ + R₂ + R₃ +... In a series circuit, if one component fails (breaks), the whole circuit stops because current path is broken. When resistors are in parallel, the voltage across each resistor is the same, but current divides. The reciprocal of total resistance is the sum of reciprocals: 1/R_p = 1/R₁ + 1/R₂ + 1/R₃ +... For two resistors in parallel, a handy shortcut is R_p = (R₁ × R₂) / (R₁ + R₂). Parallel circuits allow independent operation of appliances; if one fails, others continue to work. In household wiring, appliances are always connected in parallel so that each gets full 230 V and can be switched on or off independently.

When current flows through a resistor, electrical energy is converted into heat. This is called the heating effect of current or Joule heating. The heat H (in joules) produced is given by H = I² R t, where I is current in amperes, R is resistance in ohms and t is time in seconds. This is Joule's law of heating. Alternative forms are H = V I t (using Ohm's law V = IR) and H = V² t / R (useful when voltage is constant, as in parallel circuits). The heating effect is the basis for electric heaters, irons, geysers, toasters and filament bulbs. Materials with high resistivity and high melting points (like nichrome) are chosen for heating elements so they glow red-hot without melting. Fuses use the heating effect in reverse: a thin wire of low melting point melts and breaks the circuit when excess current flows, protecting appliances from damage.

Electric power is the rate at which electrical energy is consumed or converted into other forms. The SI unit is the watt (W), where 1 watt = 1 joule per second. The fundamental formula is P = V I (power equals voltage times current). Using Ohm's law V = I R, we derive two more useful forms: P = I² R and P = V² / R. Which form you use depends on what is given in the problem. If current is known (common in series circuits), use P = I² R. If voltage is constant (parallel circuits, household appliances), use P = V² / R. The power rating on an appliance (like '100 W, 230 V' on a bulb) tells you it consumes 100 watts when connected to 230 volts. From P = V² / R, you can find the resistance of the bulb filament. Commercial electrical energy is measured in kilowatt-hours (kWh), where 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. Electricity bills are calculated as Energy (kWh) = Power (kW) × Time (hours).

Understanding precise definitions is critical for 1-mark and 2-mark theory questions in CBSE board exams. Electric current is the rate of flow of electric charge; SI unit is ampere (A), defined as one coulomb per second. Potential difference between two points is the work done to move one coulomb of charge between those points; SI unit is volt (V). One volt = one joule per coulomb. Resistance is the opposition to current flow; SI unit is ohm (Ω). One ohm is the resistance of a conductor when a potential difference of one volt causes a current of one ampere. Resistivity is resistance per unit length per unit area; SI unit is Ω·m. An electric circuit is a closed conducting path through which current can flow. Ohmic conductors obey Ohm's law; non-ohmic do not. A combination circuit has both series and parallel parts. Write these definitions exactly as NCERT presents them for full marks in board exams, especially if the question says 'Define the term...' or 'State the SI unit of...'.

Many students lose marks in CBSE Class 10 Science board exams due to incorrect units or notation. Here is a definitive list. Charge Q is measured in coulombs (C). Current I in amperes (A). Voltage or potential difference V in volts (V). Resistance R in ohms (Ω, Greek omega). Resistivity ρ (rho) in ohm-metre (Ω·m), never ohm per metre. Time t in seconds (s) for energy and heat formulas, but hours (h) for commercial energy calculations. Power P in watts (W) or kilowatts (kW). Energy E or H in joules (J) or kilowatt-hours (kWh). Always write units in parentheses after numerical answers in board exams. Write symbols in italics or as they appear in NCERT: I for current, not i; V for voltage, not v. Use subscripts where needed: R₁, R₂ for different resistors. The symbol for resistivity is the Greek letter ρ (rho), not p. Area A is in square metres (m²); if given in mm² or cm², convert before substituting into formulas. Length L is in metres (m). One extremely common mistake is writing resistivity unit as Ω/m instead of Ω·m; this costs one full mark in definitions and numericals. Another mistake is using minutes or hours directly in H = I²Rt without converting to seconds; always convert time to seconds first.

Remembering formulas under exam pressure is easier with mnemonics and memory aids. For Ohm's law triangle, write V at the top, I and R at the bottom left and right. Cover the quantity you want to find: cover V, you see I × R; cover I, you see V / R; cover R, you see V / I. For power formulas, use the 'power triangle': write P at top, V and I at bottom. This gives P = V I. Combine with Ohm's law triangle to derive P = I² R and P = V² / R. To remember series resistance rule (add up) versus parallel (reciprocals add), think: series is simple addition, parallel is complicated (reciprocals). For heating effect, remember 'I² R t' by the phrase 'I to the square, R, time' — it rhymes and sticks. A common mistake is forgetting to square the current in H = I²Rt or P = I²R; students write I Rt and lose marks. Another is mixing up series and parallel formulas: in exams, draw a quick sketch of the circuit first. For resistivity, remember the formula as a sentence: Resistance equals Rho times Length over Area (R = ρ L / A). Many students write ρ A / L, which is dimensionally wrong. When solving numericals, always write the formula first, then substitute with units, then compute. This method-mark approach can save you even if the final answer is wrong. Finally, double-check units in your final answer; CBSE marking schemes award one mark for correct unit in 2-mark and 3-mark numericals, so never leave it blank.

Practising solved examples is the fastest way to master formula application. Here are three typical CBSE board-style numericals with complete solutions. Notice how each solution starts by writing the relevant formula, substitutes values with units, then solves step-by-step. This method earns full marks even if minor calculation errors occur. Example A tests Ohm's law and power in a straightforward way. Example B tests series combination and application of V = IR across the whole circuit and individual resistors. Example C tests parallel combination and the reciprocal formula; many students make arithmetic errors in adding fractions, so practice is essential. Always double-check your arithmetic when dealing with reciprocals. In board exams, show every step clearly; do not skip the formula statement or unit conversions. If the question says 'Calculate and show all steps', skipping steps costs marks even if the answer is correct. For 3-mark numericals, typically one mark is for writing the correct formula, one for substitution with units and one for the correct final answer with unit. Make sure your working is neat and formula statements are underlined or highlighted so the examiner can easily award method marks.

This condensed checklist is designed for quick revision in the final 24 hours before your CBSE Class 10 Science board exam. Read it once in the morning and once just before entering the exam hall. It covers every high-probability formula, definition and tip that has appeared in the last five years of board papers. Make sure you can recall each formula without looking and can state the SI unit and symbol for every quantity. Tick off each point as you revise. If you are short on time, prioritise the first five points — they cover about seventy percent of the numerical questions. For theory, focus on definitions of resistance, resistivity, Ohm's law statement and reasons why household appliances are in parallel. Practice drawing the circuit symbols for cell, resistor, ammeter and voltmeter neatly; untidy diagrams lose marks in diagram-based questions. Finally, remember that CBSETUTOR.ai offers unlimited doubt-solving by uploading a photo of any question, available 24×7 at a flat ₹999 per month for all classes 6 to 12, with a 3-day free trial — a smart investment if you want an AI tutor in your pocket during revision season.

Memorising formulas is one thing; applying them correctly under exam pressure is another. CBSETUTOR.ai gives you a 24×7 AI tutor that solves your doubts instantly by analysing a photo of any Class 10 Science numerical or theory question. Stuck on whether to use P = I²R or P = V²/R in a parallel circuit problem? Upload the question, and the AI explains step-by-step which formula applies and why. Confused about reciprocal addition in parallel resistors? The AI breaks it down with your exact numbers. The entire platform costs just ₹999 per month for unlimited questions across all subjects in Classes 6 to 12 — one flat price, no hidden fees. You get a 3-day free trial to test it during your Chapter 11 revision. Thousands of CBSE students use CBSETUTOR.ai as their personal revision coach, especially for high-weightage chapters like Electricity where numericals decide your score. The AI is trained on NCERT and past board papers, so explanations match CBSE marking schemes. Parents in metros like Delhi, Mumbai and Bangalore, as well as Tier-2 cities where coaching is expensive or unavailable, find it a cost-effective alternative to₹15,000-per-month coaching classes. Try the free trial and see how fast your formula recall and problem-solving speed improve.