Electricity and circuit tools
Ohm’s law, resistor network, voltage divider and capacitor calculators, plus DC circuit, RLC, electric field and electromagnetic induction simulators.
20 tools
Circuit work is mostly Ohm’s law and its consequences, applied often enough that the arithmetic becomes the bottleneck rather than the understanding. Most of these tools cover the calculations that come up while designing something rather than while studying.
The field simulators are the exception, and they are here because a circuit diagram deliberately says nothing about the space the current sits in. Once the question is about that space, a schematic has no answer to give and a picture of the field does.
Where a component choice is involved they report the practical answer too: the nearest standard resistor value, the power the part will actually dissipate. A mathematically correct value that no one manufactures is not a usable answer.
The theme running through all of it is that a component is not its nominal value. An E12 resistor is typically ±10 percent, a 1 percent metal film comes from the denser E96 series, aluminium electrolytic capacitors are commonly ±20 percent, and an LED’s forward voltage varies between parts from the same reel.
Simulators
Calculators
Visualisers and practice
Check the power rating, not just the resistance
Ohm’s law tells you the resistance you need. It says nothing about whether the resistor will survive, and that is a separate calculation: P = I²R, or equivalently V²/R. A quarter-watt resistor asked to dissipate half a watt will discolour, drift out of tolerance and eventually fail open.
The same LED can land either side of that line depending only on the supply. Driving a 3.2 V white LED at 20 mA from 5 V needs about 90 Ω, dissipating around 36 mW, which nothing minds. Driving the same LED at the same current from 12 V needs about 440 Ω, and that resistor dissipates about 176 mW: inside the rating of a quarter-watt part, and running at 70 percent of it.
Derate deliberately. A part rated for roughly twice the calculated dissipation costs almost nothing and stays well below the temperature at which its value shifts.
Headroom is what makes a design survive tolerance
Current through an LED is set by the voltage left over after the forward drop, divided by the resistor. When that leftover is large the circuit barely notices part-to-part variation; when it is small, everything shows. From 5 V through 90 Ω, an LED whose forward voltage turns out to be 3.4 V rather than 3.2 V drops from 20 mA to about 17.8 mA, an 11 percent change. From a 3.3 V supply the calculated resistor is around 5 Ω, and the same 3.4 V part does not light at all.
Forward voltage also depends on colour, because it tracks the band gap of the emitting material. Red parts sit near 2 V while blue and white parts are closer to 3.2 V, which is why a design that worked with a red LED can fail outright when someone fits a white one on the same 3.3 V rail.
Temperature closes the loop. Forward voltage falls as the junction warms, so a low-headroom design draws more current as it heats, which heats it further.
Why RC circuits take five time constants
Charging is exponential, so a capacitor never quite finishes. After one time constant it has reached about 63 percent of the supply, after three about 95 percent, and after five about 99.3 percent. That is close enough that five RC is the working definition of settled.
This is also the number that sets how fast a circuit can be driven. If a signal changes faster than roughly five time constants, the capacitor never reaches its final voltage and the output is a smeared version of the input. Whether that is a bug or the entire purpose depends on whether you are building a debounce circuit or a data line.
Time constant and cutoff frequency are two views of the same pair of components, related by f = 1/(2πRC). A 10 kΩ resistor with a 100 nF capacitor gives a 1 ms time constant and a 159 Hz cutoff. Note what a cutoff frequency is not: it is where the output has fallen by 3 dB, not a wall. A first-order RC filter rolls off at 20 dB per decade, so a signal ten times above the cutoff is attenuated tenfold and is still there.
Fields, where the circuit view runs out
Four of the simulators here work in the space rather than in the schematic: the electric field of a set of point charges, the path of a charge moving through a magnetic field, the field inside and around a solenoid, and the voltage a changing flux drives round a loop. Nothing in Ohm’s law answers any of those questions, which is the honest reason they are a separate group rather than more circuit tools.
The most useful fact in the magnetic pair is that the time round does not depend on the speed. A particle of mass m and charge q in a uniform field B travels a circle of radius mv/(qB), so doubling its speed doubles the radius, while the time to go round, 2πm/(qB), holds. That is why a cyclotron can drive a whole bunch of particles at one fixed frequency, and it takes one slider to watch it happen: double the speed, and the loop widens while the period stays where it was.
Induction is about flux rather than field, and that is the step that catches people. The voltage round a coil of N turns is N times the rate at which the flux through it changes, so a coil held still in a strong field produces nothing at all, and a coil turned edge-on to the field produces nothing however fast it is moved, because the flux through it is zero throughout. Move the magnet twice as fast and the voltage doubles.
Cable runs and stored charge
Voltage drop needs the length of conductor the current actually travels, which is both ways. A socket 15 metres from the supply means 30 metres of copper, and the one-way figure halves the calculated drop. Resistance also rises with temperature, by about 0.393 percent per degree Celsius for copper, so a conductor at 70 °C has roughly 20 percent more resistance than a figure built from resistivity quoted at 20 °C.
Aluminium is used for overhead lines despite conducting worse than copper, and the reason is a straight trade. Its resistivity is about 1.6 times higher, so it needs a larger cross-section for the same resistance, but it is roughly a third of the density and considerably cheaper. Where a conductor hangs between towers, mass per metre binds before conductivity does.
Stored energy is where circuit work stops being academic. Energy in a capacitor is half CV², so it scales with the square of the voltage: a 1000 µF capacitor at 400 V holds 80 joules, which is enough to kill, and it can sit charged for a long time with no load across it. Discharge a large supply capacitor through a resistor and measure it before touching anything.
Common questions
Why is my LED dimmer than the calculation predicted?
Current through the LED depends on the supply voltage minus the forward voltage, so anything that shrinks that difference shrinks the current more than it looks like it should. The three usual causes are a forward voltage higher than the datasheet typical, a resistor rounded up to the next standard value, and a supply sagging under load. With a 5 V supply and a 90 Ω resistor, a forward voltage of 3.4 V instead of 3.2 V costs about 11 percent of the current on its own. Designs with more headroom between the supply and the forward voltage are far less sensitive to all three.
How do I choose between a quarter-watt and a half-watt resistor?
Work out the dissipation with P = I²R, then pick a part rated for roughly twice that figure. A resistor run at its nominal rating is not failing, but it is hot enough to drift out of tolerance and to discolour the board around it, and the drift is often permanent. Bear in mind that the rating assumes reasonable airflow and that physical size is what actually sheds the heat, so a small surface-mount part at its rated power runs hotter than a larger part at the same power.