Ohm’s Law & Circuit Calculator

Solve V = IR from any two values, build series and parallel resistor circuits with a live diagram, decode resistor colour bands and estimate your electricity bill.

Class 10–12 Electricity chapter Series & parallel Colour code

Ohm's law says that at constant temperature, the current through a conductor is directly proportional to the potential difference across it: V = I × R. A 6 Ω coil on 12 V draws I = 12 ÷ 6 = 2 A and uses P = VI = 24 W. In series R = R₁ + R₂; in parallel 1/R = 1/R₁ + 1/R₂.

Enter any two values

Leave the other two blank — they are worked out for you.

Try an example

Results

Red values are calculated; navy values are the ones you entered.

Formula triangles

Tap a letter to “cover” it — the letters left show its formula. Side by side = multiply, one above the other = divide.

Step-by-step working

    How it works

    Understand every part of a circuit

    From a single torch bulb to your home’s monthly bill — the same three ideas (V = IR, series and parallel) explain it all.

    Ohm’s law

    Type any two of V, I, R and P in any unit — the other two appear with full working.

    Build a network

    Pick series, parallel or groups, add resistors and a battery voltage to see the diagram and every current.

    Decode colours

    Tap the four band colours to read a resistor’s value and tolerance — or go the other way.

    Check the bill

    List your appliances, hours of use and rate per unit to see where the units go.

    Ohm’s law and power

    V = I × R   P = V × I = I²R = V²/R

    Example: a 6 Ω heater coil on a 12 V supply draws I = 12 ÷ 6 = 2 A and uses P = 12 × 2 = 24 W.

    Resistors in series

    Rs = R₁ + R₂ + R₃ + …

    The same current flows through each resistor; the battery voltage is shared, V = V₁ + V₂ + V₃. The total is always bigger than the largest resistor.

    Resistors in parallel

    1/Rp = 1/R₁ + 1/R₂ + …

    Each resistor gets the same voltage; the currents add up, I = I₁ + I₂ + …. The total is always smaller than the smallest resistor. Two resistors: R = R₁R₂ ÷ (R₁ + R₂).

    Why homes use parallel wiring

    Every appliance gets the full 220–230 V, each can be switched on or off independently, and if one fails the others keep working. Energy used: 1 unit = 1 kWh = 3.6 × 10⁶ J.

    Safety first: the 220 V mains supply can kill. Try circuits only with 1.5 V cells and a torch bulb, and never open a plug, socket or appliance that is connected to the mains.
    Questions & answers

    Ohm’s Law & Circuit Calculator — your questions

    What is Ohm's law and its formula?

    Ohm's law says that at constant temperature the current through a conductor is directly proportional to the potential difference across its ends, so V = I × R. Voltage is in volts, current in amperes and resistance in ohms. Rearranged, I = V ÷ R and R = V ÷ I. A graph of V against I is a straight line through the origin.

    How do you find equivalent resistance in series and parallel?

    In series, add them: Rs = R₁ + R₂ + R₃, so 6 Ω and 3 Ω in series give 9 Ω. In parallel, add the reciprocals: 1/Rp = 1/R₁ + 1/R₂, so 6 Ω and 3 Ω in parallel give 2 Ω. Series resistance is always larger than the biggest resistor; parallel resistance is always smaller than the smallest.

    Why are home appliances connected in parallel?

    In parallel every appliance receives the full 220 to 230 V it is designed for, each can be switched on and off independently, and if one fails the rest keep working. In series they would share the voltage, run below their rating and all go off together — which is why old decorative light strings failed completely when one bulb blew.

    What are the formulas for electric power?

    Power can be written three ways: P = V × I, P = I²R and P = V² ÷ R, all in watts. Use whichever matches the quantities you are given. Energy used is E = P × t, and when power is in kilowatts and time in hours the answer comes out directly in commercial units (kWh).

    How do you read resistor colour bands?

    Hold the resistor with the gold or silver tolerance band on the right and read from the left. The first two bands are digits, the third is the multiplier and the fourth is the tolerance. Remember the digit order 0 to 9 with the sentence "BROY of Great Britain had a Very Good Wife" — black, brown, red, orange, yellow, green, blue, violet, grey, white.

    How is an electricity bill calculated?

    One unit is one kilowatt-hour, the energy used by a 1000 W appliance in one hour. Multiply each appliance's power in kilowatts by the hours it runs to get units, add them for the month, then multiply by the rate per unit and add any fixed charge. One unit equals 3.6 × 10⁶ joules.

    Is the current the same in series and parallel circuits?

    In a series circuit the same current passes through every component and the supply voltage is shared between them. In a parallel circuit every branch gets the same voltage and the branch currents add up to the total. This is why an ammeter goes in series, while a voltmeter is connected in parallel across a component.