NCERT Class 10 Science — Chapter 11, Electricity
How do you find the current in a series and a parallel circuit?
Combine the resistors into a single equivalent resistance first, then apply Ohm's law, I = V/R. In series, resistances simply add: R = R₁ + R₂. In parallel, the reciprocals add: 1/R = 1/R₁ + 1/R₂, which always gives a resistance smaller than the smallest individual resistor.
Do the combining before the Ohm's law, always
The order matters. Students who apply I = V/R to individual resistors before combining them end up with currents that do not add up, then try to patch the result. Reduce the network to one equivalent resistance first, find the total current, and only then work back to individual branches if the question asks.
A useful sanity check: a parallel combination is always smaller than the smallest resistor in it. If your parallel answer is bigger than any individual resistor, you have added instead of taking reciprocals.
Why parallel resistance goes down, not up
This is worth understanding rather than memorising. Adding a resistor in parallel gives the current an extra path to flow through. More paths means more total current for the same voltage, and more current for the same voltage is, by definition, less resistance.
The same physical reasoning explains why household appliances are wired in parallel: each one gets the full supply voltage, and switching one off does not break the path for the others.
Power, and the units question examiners like
Once you have V and I, power is P = VI, which can also be written as I²R or V²/R depending on what the question gives you. All three are the same relationship with Ohm's law substituted in.
Watch the units. A rating in kilowatt-hours is energy, not power — it is a power multiplied by a time, which is exactly the calculation an electricity bill performs.
A worked example
Three resistors of 4 Ω, 6 Ω and 12 Ω are connected in parallel across a 12 V battery. Find the equivalent resistance and the total current.
- Combine the resistors1/R = 1/R₁ + 1/R₂ + …4Ω ∥ 6Ω ∥ 12Ω → R = 2 Ω
- Ohm's lawI = V / RI = 12 / 2 = 6 A
- PowerP = V·IP = 72 W
⚙️ Every number above was computed by Bolo’s Circuit Builder engine when this page was built — the same code that checks your answer inside the app, not a hand-typed solution.
Now try it yourself
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Open the Circuit Builder →Common questions
Is the current the same everywhere in a series circuit?
Yes. There is only one path, so the same charge passes through every component in turn. What differs is the voltage dropped across each resistor, which is proportional to its resistance. In a parallel circuit the opposite holds: voltage is shared equally, current divides.
Why is the equivalent resistance in parallel smaller than each resistor?
Because each extra branch gives current another route. More available paths means more total current flows for the same voltage, and by Ohm's law more current at fixed voltage means less resistance. The combination is always smaller than the smallest branch.
Why are home appliances connected in parallel?
Two reasons. Each appliance receives the full supply voltage it is rated for, and each can be switched off independently without breaking the circuit for the others. In series, one failed bulb would open the circuit and everything would stop working.