Home / Learn / Physics / Series and parallelTool #L17 (formerly #1042)

Series and parallel

Drag four resistors into series, into a parallel box or out of the circuit. The page works out the equivalent resistance step by step, shows the current splitting with moving dots, and gives the voltage, current and power for each resistor, plus the energy used in kWh and its cost.

Keep it one tap away for everyday use.

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  1. Drag
  2. Work out
  3. Watch flow
  4. Bill
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Build the circuit

Drag a resistor onto the top wire to put it in series, into the box below to put it in parallel, or down to the tray to take it out. The dots show the current: they move faster where more current flows.

Worked out step by step

    Energy and the bill

    The price is only an example: use the rate per unit on your own electricity bill. 1 unit = 1 kWh.

    Try this

    • Put all four in series. The total is the sum, and the same current flows through each one.
    • Now drag them all into the parallel box. The total is smaller than the smallest one, and each gets the full battery voltage.
    • Two equal resistors in parallel give half of one. Try 10 Ω and 10 Ω.
    • Pick 230 V and put resistors in parallel, the way a house is wired: each appliance gets 230 V and can be switched on its own. Watch the power and the bill.
    • At Class 12, raise the internal resistance: the terminal voltage falls when more current flows.

    Check yourself

    What it does

    This page is a circuit board with four resistors and a battery. Drag a resistor onto the top wire and it is in series: the same current goes through it and everything else. Drag it into the box below and it joins the parallel bank: it gets the same voltage as the others in the box and takes its own share of the current. Drag it down to the tray and it is out of the circuit.

    As you build, the page works out the equivalent resistance one step at a time (series part, parallel part, total), then the current from the battery, the voltage across the parallel box, the current in each branch and the power. Dots move round the wires, faster where more current flows, so you can see the current split at a junction and join up again.

    It follows the Class 10 Science electricity topics (resistors in series and in parallel, the heating effect, electric power and the kilowatt hour) and, with the Level switch on Class 12, the Class 12 Physics current electricity topics (internal resistance, terminal voltage, Kirchhoff’s rules). If you have not met V = IR yet, start with the ohm's law lab; to try bigger circuits with switches and other parts, go on to the circuit simulator.

    How to use it

    1. Choose the battery voltage. 230 V is the voltage of house wiring in India, for working out appliance power and bills.
    2. Drag the resistors R1 to R4 around the picture, or use the table under it: type each resistance in ohms and pick Series, Parallel or Not used.
    3. Read Worked out step by step. The table under it gives the voltage across, the current through and the power in each resistor.
    4. In Energy and the bill, type how many hours a day the circuit is on, for how many days, and the price of one unit (1 kWh). The page gives the energy and the cost.
    5. Switch the Level to Class 12 to give the battery an internal resistance r. The page then shows the terminal voltage, the volts lost inside the battery and Kirchhoff’s loop rule with your numbers.

    Worked example

    The page starts with R1 = 10 Ω on the top wire, R2 = 10 Ω and R3 = 15 Ω in the parallel box, and a 6 V battery.

    • Parallel box: 1/R_p = 1/10 + 1/15 = 0.1667 per Ω, so R_p = 6 Ω.
    • Total: R = 10 + 6 = 16 Ω.
    • Current: I = 6 / 16 = 375 mA. R1 has 3.75 V across it; the parallel box has 2.25 V.
    • The 375 mA splits: 225 mA through R2 and 150 mA through R3, and 225 + 150 = 375.
    • Power: 6 V × 0.375 A = 2.25 W. On for 5 hours a day for 30 days, that is 0.338 kWh, which costs about ₹2.36 at ₹7 a unit.

    Tips

    • In series the total is always bigger than the biggest resistor; in parallel it is always smaller than the smallest one.
    • For two resistors in parallel, product over sum is a quick shortcut: 6 × 3 / (6 + 3) = 2 Ω.
    • If nothing is in the circuit the page warns about a short circuit, which is what a fuse protects a house from.

    FAQ

    Why are houses wired in parallel? Each appliance gets the full 230 V and can be switched on or off without affecting the others. In series, one switched-off lamp would turn everything off.

    Is the price per unit real? No, ₹7 is only a starting example. Type the rate from your own bill.

    Is anything saved? No. The circuit and your answers stay on this page and are gone when you close it.

    Where the numbers come from

    • Resistors in series (R = R₁ + R₂ + ...) and in parallel (1/R = 1/R₁ + 1/R₂ + ...), P = VI = I²R, energy in kWh, and Kirchhoff's junction and loop rules with a battery's internal resistance: standard school physics results.
    • The price per kWh is a made-up example that you can change; no tariff data is used.
    • Checked against an independent Python script (fractions for exact parallel sums, then the currents, voltages and powers) and hand-worked examples such as 6 Ω ∥ 3 Ω = 2 Ω.

    Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

    Last updated 2026-11-09.

    Change log for Series and parallel

    1. Add #1042 Series and parallel circuit builder Details on GitHub

    Every change to fibub

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