Series and Parallel Circuit Simulator
Equations in this simulation
| V | voltage across a component | the drop in electric potential from one end to the other, in volts | |
|---|---|---|---|
| I | current through it | in amperes: the charge passing per second | |
| R | R₁ (ohms) | Ohm's law holds for each resistor; a real filament's resistance rises as it heats, which is left out |
With the current values:
| R_eq | equivalent resistance of everything outside the battery | in series the same current flows through each, in parallel each sees the same voltage |
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With the current values:
| KCL, KVL | Kirchhoff's current and voltage laws | charge is not created or lost at a junction, and energy per charge balances round any closed loop; the simulation solves them for every node at once |
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With the current values:
| E | Battery voltage E (volts) | the electromotive force, what the battery would read with nothing connected | |
|---|---|---|---|
| r | Internal resistance of the battery r (ohms) | drops some voltage inside the battery, more the more current is drawn |
With the current values:
| P | power turned into heat and light | the bulbs glow with it; the chart shows how much R₁ takes as its resistance changes, largest when it matches the rest of the circuit |
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With the current values:
| V_out | divider output, or the meter voltage in the bridge | without a load for the divider; a load in parallel with R₂ pulls V_out down, and a balanced bridge reads zero |
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With the current values:
How to use the circuit simulator
- Pick a circuit. The battery is on the left with its + plate marked; the bulbs glow with the power they take, and the blue dots are electrons drifting from the − terminal round to the +, faster where the current is larger. Conventional current, the direction the formulas use, runs the other way.
- Change the battery voltage and each resistance, and read the current, voltage and power of every bulb under the picture. Open the switch to break one branch: in series everything goes dark, in parallel the other bulbs carry on. The chart shows how much power R₁ takes as its resistance changes, with a peak where it matches the rest of the circuit.
- Try the voltage divider and watch the output fall as the load is connected, or the Wheatstone bridge and find the R₄ that makes the meter read zero. The Ohm's Law Calculator, Series and Parallel Calculator and Voltage Divider Calculator do the same sums for your own values.
Frequently asked questions
What is the difference between series and parallel circuits?
In series the components are in one line, so the same current flows through each and the voltages add up to the battery's: R = R₁ + R₂ + …. In parallel each component has its own path between the same two points, so each gets the full voltage and the currents add up: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + …. Parallel is how houses are wired, so every lamp gets mains voltage and one can be switched off without the rest.
What are Kirchhoff's laws?
The current law: the currents flowing into any junction equal the currents flowing out, because charge does not pile up. The voltage law: going round any closed loop, the voltage rises and drops add up to zero, because energy per charge has to balance. Together with Ohm's law they solve any circuit of resistors and batteries, which is what the simulation does at every node.
Why does the battery voltage drop when more bulbs are connected?
A real battery has internal resistance r. The current drawn drops I × r volts inside the battery, so the terminal voltage is E − I r. Connecting bulbs in parallel lowers the total resistance and raises the current, so the drop grows. Set r to 0 to see an ideal battery.
How fast do electrons move in a wire?
Slowly: in a copper wire 1 mm across carrying 1 A they drift at under a tenth of a millimeter per second. The bulb lights at once because the electric field travels through the circuit at nearly the speed of light and sets all the electrons moving together. The dots here are speeded up enormously to show the relative currents.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.