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Electricity carries a large share of the Class 10 physics marks, and most of them come from numericals. Students often know V = IR but freeze when three resistors are drawn in a mix of series and parallel. The fix is a fixed order of steps that works on every circuit in the chapter. This post walks through it with a full example, explains the most common wrong idea about circuits, and gives you a practice plan.
What does the syllabus include?
The CBSE Class X Science syllabus for 2026-27 lists, under Unit IV, Effects of Current (13 marks): electric current and potential difference, Ohm's law, resistance and resistivity and the factors they depend on, series and parallel combinations, the heating effect of current, and electric power and the relation between P, V, I and R. Two practicals come from this chapter: plotting V against I for a resistor, and finding the equivalent resistance of two resistors in series and in parallel. The formulas and values below are from Chapter 11 of the NCERT Class 10 Science textbook. Check the syllabus for your year.
Which formulas do you actually need?
Ohm's law: V = IR, at constant temperature.
Resistance of a wire: R = ρl/A, where ρ is the resistivity of the material, l the length and A the cross-sectional area.
Series: R = R₁ + R₂ + R₃. The same current flows through each resistor.
Parallel: 1/R = 1/R₁ + 1/R₂ + 1/R₃. Each resistor has the same potential difference across it.
Power: P = VI = I²R = V²/R. Heat produced: H = I²Rt (Joule's law of heating).
Energy bills: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. One kWh is the "unit" on an electricity bill.
A worked circuit, step by step
Problem. Two 6 Ω resistors are connected in parallel. This pair is connected in series with a 2 Ω resistor across a 10 V battery. Find the current from the battery, the potential difference across each part, the current in each 6 Ω resistor, and the total power.
Reduce the parallel pair. 1/R = 1/6 + 1/6 = 2/6, so R = 3 Ω.
Add the series part. Total resistance = 3 + 2 = 5 Ω.
Find the total current. I = V/R = 10/5 = 2 A.
Work back to each part. Across the 2 Ω resistor: V = 2 × 2 = 4 V. Across the parallel pair: V = 2 × 3 = 6 V. Check: 4 + 6 = 10 V, the battery voltage.
Split the current. Each 6 Ω resistor has 6 V across it, so each carries 6/6 = 1 A. Check: 1 + 1 = 2 A.
Find the power. P = VI = 10 × 2 = 20 W. Check with I²R: 2 Ω resistor, 2² × 2 = 8 W; each 6 Ω resistor, 1² × 6 = 6 W. Total 8 + 6 + 6 = 20 W.
The checks in steps 4, 5 and 6 take a few seconds and catch most arithmetic slips.
A quick energy question. A 1500 W heater runs 2 hours a day for 30 days. Energy = 1.5 kW × 60 h = 90 kWh, or 90 units.
A resistivity question. A wire is stretched to twice its length. Its volume stays the same, so its area halves. R = ρl/A becomes ρ(2l)/(A/2) = 4ρl/A. The resistance becomes four times the original, not two.
Why do students get circuits wrong?
Cohen, Eylon and Ganiel (1983) gave a questionnaire to 145 high-school students and 21 physics teachers. They found that students treated current as the main idea and saw potential difference as a result of current rather than its cause. Many thought of a battery as a source of constant current, and found it hard to work out how changing one component affects the rest of the circuit.
For Class 10, that shows up in mistakes like these:
Assuming the current stays the same when you add a resistor. The battery's potential difference stays fixed; the current changes.
Adding parallel resistances directly. Two 6 Ω resistors in parallel give 3 Ω, less than either one.
Forgetting to invert at the end. 1/R = 1/3 means R = 3 Ω, not 1/3 Ω.
Mixing units. Convert kilowatts and hours before computing kWh; convert mm² to m² before using R = ρl/A.
NCERT's Table 11.2 shows why heating elements use alloys. Nichrome has a resistivity of 100 × 10⁻⁶ Ω m, against 1.62 × 10⁻⁸ Ω m for copper, and alloys do not oxidise readily at high temperature.
A practice routine for this chapter
Week 1: Ten Ohm's law and resistivity questions, including two "stretched wire" problems.
Week 2: Eight mixed series-parallel circuits. Write all six steps for each, including the checks.
Week 3: Power and energy: five bill calculations and five heating-effect questions using H = I²Rt.
Before the exam: For each circuit you got wrong, write one sentence on which step failed.
If you are unsure whether you chose the right method, compare your reasoning against a full solution. The Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer. To see how current divides as you change resistors, try the Fermi Simulation Lab. When you are done, the next chapter is magnetic effects of current.
Tonight, solve one series-parallel circuit using all six steps, including the checks.
