Experiment
Circuitcurrent, voltage and resistance
Build your own circuit on the board: batteries, bulbs, resistors, diodes, capacitors. The simulator keeps computing the current in every wire — watch the charges flow, see which bulb shines brightest and what burns out.
- U = R·IOhm's law
- ΣI = 0Kirchhoff's laws
- P = U·Ipower
- τ = R·Ccapacitor
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Capacitor voltage U(t)
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Challenges
0 / 4Did you know…?
In a copper wire with a 1 mm² cross-section carrying 1 A, electrons drift on average by about 0.07 mm per second — slower than a snail. Yet the lamp lights up instantly, because the electric field travels along the wires at nearly the speed of light and pushes electrons through the whole circuit at once.
The conventional direction of current (from + to −) was fixed before the electron was discovered — J. J. Thomson did that only in 1897. It turned out that in metals negative charges flow, i.e. the opposite way. The convention stayed, because all the calculations come out the same.
A cold bulb filament has about 10–15 times lower resistance than one glowing at over 2000 °C. So at the moment you switch it on, the current can be more than ten times the rated value — which is why bulbs most often burn out right when they are turned on.
How does it work?
1 Current, voltage, resistance
Current is an orderly flow of charges. Its magnitude I tells you how much charge passes each second (1 A = 1 C/s). Voltage U is the potential difference between two points — a battery creates it the way a pump creates a pressure difference. Resistance R tells you how strongly a part opposes the flow.
Wire colors show the potential: from blue (battery minus, 0 V) to red (plus).
2 Kirchhoff's laws
First law (junctions): as much current flows into a junction as flows out of it — charge doesn't vanish or pile up in the wires.
Second law (loops): going around any closed loop, the voltage rises and drops add up to zero. The battery voltage is shared among the parts along the way.
3 Power and brightness
Power is the energy converted every second. The more power a bulb gets, the brighter it shines.
A “6 V · 3 W” bulb has a resistance of R = U²/P = 12 Ω. Half the voltage gives a quarter of the power. Here a bulb burns out when it gets more than 150% of its rated power.
4 Series and parallel
In series the same current flows and the voltages add up. In parallel every branch has the same voltage and the currents add up.
Voltage divider: U2 = U · R₂ / (R₁ + R₂). You get 3 V out of 9 V when R₁ = 2·R₂.
5 Capacitor and time constant
A capacitor stores charge Q = C·U and energy E = ½·C·U². Charged through a resistor, it gains voltage more and more slowly:
After a time τ the voltage reaches 63.2% of its final value (1 − 1/e), and after 5τ — 99.3%. In the steady state no current flows: the capacitor acts like a gap.
6 LED and Wheatstone bridge
An LED conducts only one way: from the anode (+) to the cathode (the bar on the symbol). It lights up only above its forward voltage (red about 1.8 V, blue about 3 V), and then the current rises exponentially — which is why it always needs a resistor:
The bridge is balanced when R₁/R₂ = R₃/R₄ — then no current flows through the ammeter in the middle.
7 How does the simulator compute?
After every change the simulator sets up equations using modified nodal analysis (MNA): Kirchhoff's first law for each node and one equation for each voltage source. It solves them by Gaussian elimination. The diode follows the Shockley equation I = Is(eU/nUT − 1), so it is solved iteratively with Newton's method. The capacitor is computed step by step every 2 ms or so (implicit Euler method).
Simplifications: a bulb has a constant resistance (in reality it grows with the filament temperature), a wire has 0.1 mΩ, an ammeter 1 mΩ, a voltmeter 10 MΩ, and a battery a small internal resistance (0.1 Ω by default). A reverse-biased diode never breaks down, and parts burn out the instant they pass their limit. The speed of the dots is only relative.