Circuits Dynamic

Circuits Dynamic uses advanced mathematics (matrix/linear algebra and numerical integration/methods) to solve circuits with wires, switches, batteries, resistors, capacitors, and inductors.
A stylus pen is strongly recommended, but not strictly required.
There is also a desktop circuit solver at freecircuitsolver.com. It works better than the mobile version and has been heavily tested. If you like either version, please share it.

Key:
- ΔV: represents a potential drop between nodes. Volts are measured in units of energy (i.e. joules) per charge (coulombs).
- I: current, measured in amps (A) measures a rate of flow of charge. An amp represents one coulomb per second.
- R: resistance is measured in ohms (Ω) and can be used to calculate a voltage drop across a component given the current.
- ε: electromotive force (emf), a force that propels charge though a circuit
- Q: charge, measured in coulombs (C)
- C: capacitance, measured in farads (F)
- I': rate of change of current (A / sec)
- L: inductance, measured in henries (H)
- φ: magnetic flux

Components:
- resistor: ΔV = I R
- battery (voltage source): ΔV = ε
- wire: ΔV = 0
- capacitor: Q = C V
- inductor: ΔV = L I', φ = L I
- switch: closed ΔV = 0, open I = 0
- ammeter: measures current in amps (A)
- ohmmeter: measures equivalent resistance (be careful with these as they work by actively pumping a current through the circuit so that V= I R becomes R = V) These are intended to exist as part of a complete circuit. If you do otherwise you can create errors in other parts of the circuit.
- voltmeter: measures a voltage or potential drop between two nodes
- capacitance meter: measures equivalent capacitance (be careful with these as they work similarly to ohmmeters)
- inductance meter: measures equivalent capacitance (be careful with these as with ohmmeters and capacitance meters)
- current source: dual to a battery, they carry a pre-specified current. Be sure to complete circuits containing current sources, or else you will introduce an inconsistency into the system, which can carry over to other parts of the circuit.
- current integrator / charge counter: measure the amount of charge that goes through the meter, whether in an instant (e.g. connecting capacitors directly to batteries) or over time (e.g. with a resistor present)
- voltage integrator / magnetic flux counter: measures the magnetic flux, which can be measured in volt seconds that is across the a component such as an inductor. φ = L I. The magnetic flux across an inductor is proportional to the current through it.

Modes:
-drag is for panning and zooming the screen, usually not needed.
-make is for making the type of components currently selected.
-edit is for changing the numerical value of components with a value.
-switch is for toggling switches
-delete is for deleting components. Be careful that you don't accidentally delete components which you don't intend to delete.
- animate (drag) is for progressing time, either for e.g. instantaneous currents (as when a capacitor is connected directly to a battery), or for continuous changing values.

Tips:
Draw one circuit at a time to prevent inconsistencies from propagating through the matrix. Shorted out batteries, and loose current sources create inconsistencies.
Orient your circuits vertically rather than horizontally so that meter values do not overlap.
Matrix epsilon specifies that any smaller number in the matrix is rounded down to 0. Matrix epsilon must be decreased for circuits with smaller values in the matrix.
Delta t specifies the time step the algorithm takes from step to step.
You can use scientific notation such as 1E3 for one thousand.
Full disclosure: this program does not work with all circuits such as those with very small numbers or very large numbers-this is a weakness in the mathematical algorithms employed.