Electricity & MagnetismV = IR

DC Circuits Simulator

Build simple series and parallel resistor circuits. Adjust resistances and voltage to see current distribution using Ohm's law and Kirchhoff's rules.

Parameters

Voltage V

R₁

R₂

R₃

Derived

R₂ ∥ R₃0.00 Ω

R_total0.00 Ω

V12.0 V

R_total0.00 Ω

I_total0.000 A

I₂0.000 A

I₃0.000 A

P_total0.000 W

P_R10.000 W

P_R20.000 W

P_R30.000 W

About DC Circuits

A direct-current (DC) circuit carries charge in one direction only. The fundamental law governing DC circuits is Ohm's Law: V = IR. For multi-element networks, Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) describe how voltages and currents distribute.

ℹThis simulator shows a series-parallel network: R1 in series with the parallel combination of R2 and R3. Current splits at the junction and recombines.

Key Concepts

Concept	Series	Parallel
Total Resistance	R = R₁ + R₂ + …	1/R = 1/R₁ + 1/R₂ + …
Current	Same through all	Splits between branches
Voltage	Divides among elements	Same across all branches
Power	P = VI = I²R = V²/R	P = VI = I²R = V²/R

Kirchhoff's Laws

KCL states that the sum of currents entering any node equals the sum leaving. KVL states that the sum of voltage drops around any closed loop is zero. Together they allow solving any linear DC network.

💡Make R2 very large (100 Ω) to effectively open-circuit that branch. All current then flows through R3, and vice versa.

Key Formulas

Ohm's Law

V = I R

Parallel Resistance

R_{∥} = \frac{R _{2} R _{3}}{R _{2} + R _{3}}

Total Circuit Resistance

R_{total} = R_{1} + R_{∥}

Power Dissipated

P = V I = I^{2} R = \frac{V ^{2}}{R}

ℹTotal power delivered by the source equals the sum of power dissipated in all resistors: P_total = P_R1 + P_R2 + P_R3.

Frequently Asked Questions

Why does current split unequally through R2 and R3?

In a parallel branch, both resistors share the same voltage. The current through each is I = V/R, so the lower resistance carries more current — current follows the path of least resistance.

What happens to total resistance when R2 is placed in parallel with R3?

The parallel combination is always less than either individual resistor. Adding a parallel path provides an additional route for current, reducing the total opposition to flow.

How is power conserved in this circuit?

The power delivered by the voltage source equals V × I_total. This equals the sum of I²R for every resistor. Energy is conserved — all electrical power becomes heat in the resistors.

What is Kirchhoff's Current Law and where does it apply here?

KCL says current in = current out at every node. At the junction before R2 and R3, I_total splits into I2 + I3. They recombine after the parallel section, so I_total flows through R1.