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DC Circuit Analysis Calculator

Analyse series and parallel resistor circuits. Type a network such as 100 + 220 || 330, choose a voltage or current source, and the calculator finds the equivalent resistance and the current, voltage and power for every resistor. It draws the circuit and shows each step. An Ohm's law mode solves for V, I, R or P from any two of them.

Physics · ElectricityUpdated Sources cited

Calculation
Use + for series and || for parallel, with brackets for groups. Values are in ohms and can use k and M: 4.7k, 2k2, 1M.
Source
Examples:

Result

Equivalent resistance
232 Ω
Total current
51.72 mA
Source voltage
12 V
Total power
620.7 mW
12 VR1100 ΩR2220 ΩR3330 Ω
ResistorResistanceVoltageCurrentPower
R1100 Ω5.172 V51.72 mA267.5 mW
R2220 Ω6.828 V31.03 mA211.9 mW
R3330 Ω6.828 V20.69 mA141.3 mW
Assumptions behind this result
  • Ideal source and connecting wires with no resistance.
  • Resistors are ohmic, and the network reduces to series and parallel combinations.

Step-by-step solution

  1. Combine R2 ∥ R3 in parallel

    For resistances in parallel, the reciprocals add, because the current divides between the branches.

    1R=1220+1330⇒R=132 Ω\frac{1}{R} = \frac{1}{220} + \frac{1}{330} \Rightarrow R = 132\ \Omega

  2. Combine R1 + (R2 ∥ R3) in series

    Resistances in series add, because the same current passes through each one.

    R=100+132=232 ΩR = 100 + 132 = 232\ \Omega

  3. Find the total current

    Apply Ohm’s law to the whole network.

    I=VReq=12232=0.051724 AI = \frac{V}{R_{eq}} = \frac{12}{232} = 0.051724\ \text{A}

  4. Work out each resistor

    Components in series share the same current and split the voltage; branches in parallel share the same voltage and split the current. Then V = IR and P = VI for each resistor.

    R1:  V=5.1724 V,  I=0.051724 A,  P=0.26754 WR2:  V=6.8276 V,  I=0.031034 A,  P=0.21189 WR3:  V=6.8276 V,  I=0.02069 A,  P=0.14126 W\begin{aligned} \text{R1}: \; V &= 5.1724\ \text{V}, \; I = 0.051724\ \text{A}, \; P = 0.26754\ \text{W} \\ \text{R2}: \; V &= 6.8276\ \text{V}, \; I = 0.031034\ \text{A}, \; P = 0.21189\ \text{W} \\ \text{R3}: \; V &= 6.8276\ \text{V}, \; I = 0.02069\ \text{A}, \; P = 0.14126\ \text{W} \end{aligned}

  5. Check that the power balances

    The power supplied by the source equals the total power dissipated in the resistors.

    Psource=VI=0.62069 W=0.26754+0.21189+0.14126P_{source} = VI = 0.62069\ \text{W} = 0.26754 + 0.21189 + 0.14126

What the calculator does

  • Network mode: reduces any series–parallel combination of up to 24 resistors to one equivalent resistance, then works back out to find the current, voltage and power for each resistor. It checks that the power dissipated equals the power supplied.
  • Ohm’s law mode: enter any two of voltage, current, resistance and power to find the other two.

The rules

Resistors in series carry the same current, and their resistances add:

Rseries=R1+R2+⋯R_\text{series} = R_1 + R_2 + \cdots

Resistors in parallel share the same voltage, and their conductances add:

1Rparallel=1R1+1R2+⋯\frac{1}{R_\text{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots

Ohm’s law and the power relations link everything together:

V=IR,P=VI=I2R=V2RV = IR, \qquad P = VI = I^2R = \frac{V^2}{R}

Worked example: 100 Ω + (220 Ω ∥ 330 Ω) on 12 V

  1. Parallel pair: 1/(1/220 + 1/330) = 132 Ω.
  2. Total: 100 + 132 = 232 Ω.
  3. Supply current: I = 12 / 232 = 51.7 mA. All of it flows through R1.
  4. Voltages: R1 drops 5.17 V, leaving 6.83 V across the parallel pair.
  5. Branch currents: R2 carries 31.0 mA and R3 carries 20.7 mA. Together they make up the 51.7 mA.
  6. Power check: the source supplies 621 mW and the resistors dissipate 621 mW in total.

Common mistakes

  • Adding parallel resistances directly. Add the reciprocals, then take the reciprocal of the sum.
  • Forgetting the final reciprocal, which leaves an answer in siemens rather than ohms.
  • Assuming every resistor has the full supply voltage. That is only true for resistors connected directly across the source.
  • Mixing kΩ and Ω, or mA and A. The calculator accepts prefixes and shows results in engineering units.

Practical applications

  • Voltage dividers for sensors and setting reference voltages.
  • LED current limiting, choosing a series resistor.
  • Checking power ratings before building a circuit.
  • Electronics coursework, where series–parallel reduction is a core skill.

Assumptions and limitations

The calculator models ideal resistors, ideal wires and a single ideal DC source, either a voltage source or a current source. Only circuits that reduce step by step to series and parallel combinations are supported; bridges, multiple sources, capacitors, inductors and AC analysis are not. Resistance is treated as constant, although real resistors change slightly with temperature. Results are computed in double precision.

Frequently asked questions

How do I type a circuit?

Use + for series and || for parallel. || binds more tightly than +, as multiplication does in arithmetic, so 100 + 220 || 330 means 100 Ω in series with the parallel pair. Use brackets to group differently, for example (100 + 220) || 330. Prefixes such as 4.7k, 2k2 and 1M are accepted.

Why is the parallel resistance smaller than either resistor?

Each parallel branch gives the current another path, so the combination conducts more easily than any single branch. The equivalent resistance is always less than the smallest resistor in the group.

Can it solve bridge circuits?

Not yet. Bridges such as the Wheatstone bridge, and circuits with more than one source, cannot be reduced to series and parallel steps. They need nodal or mesh analysis, which is planned.

How do I know whether a resistor will overheat?

Compare the calculated power with the resistor's power rating, commonly 0.25 W or 0.5 W for small through-hole resistors. A safety margin of about 2× is usual.

Is the source ideal?

Yes. The voltage source has no internal resistance and the wires have none either. To model a real battery, add its internal resistance in series.

References

  1. Horowitz, P. & Hill, W. (2015). The Art of Electronics (3rd ed.), chapter 1. Cambridge University Press.
  2. Young, H. D. & Freedman, R. A. (2019). University Physics (15th ed.), chapters 25–26. Pearson.
  3. IEC 60617: Graphical symbols for diagrams.

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