⚡ Capacitor Toolkit

Capacitor Charge & Discharge — Help

What You See

A circuit with a supply, two resistors, a two-way switch and a capacitor. R₁ is in the charging path and R₂ is in the discharging path, so each can set its own time constant. You can view the movement of the free electrons around the circuit, and a green arrow shows the direction and magnitude of the conventional current.

Controls

R₁, R₂, C, V — set the two resistances, the capacitance and the supply voltage with the sliders. The time constant updates live.

Charge / Isolate / Discharge — throw the switch to watch the capacitor charge through R₁, discharge through R₂, or isolate it from the circuit so it holds its charge.

Reset — empty the capacitor and return to the start.

The exponential change

While charging, the charge and the potential difference across the capacitor increase towards their final values while the current decays exponentially towards zero; discharging is an exponential decay of all three. The change is fast at first and slows as it goes, approaching the final value asymptotically. After one time constant a charging capacitor has reached about 63% of its final charge and potential difference; after one time constant a discharging capacitor has fallen to about 37% of its initial charge, potential difference and current. Once the change is effectively complete a Review slider appears — drag it to move through the run at any point, forwards or back.

Graphs

Graphs — open a floating window plotting charge, voltage, current or energy against time, plus a charge-against-voltage view. The dashed line marks one time constant. On the charge graph you can show the current underneath with a moving tangent, and a scrubber links a point on the curve to its slope. Drag the window by its header; resize from the corner.

Meters

Voltmeter — drop it on, then drag its two probes onto the circuit to read a potential difference. Energy — drop it on and touch its probe to the cell, capacitor or a resistor to read the energy supplied, stored or dissipated.

Removing an instrument — press and hold the body of a voltmeter or energy meter for a moment (or right-click on a computer) to take it off the circuit.

Display options

The various display options under the drawing canvas let you choose, for each quantity, whether to show its Value, just its Symbol, or to Hide it altogether. When a quantity is set to show only its symbol, tapping that symbol on the circuit reveals its value — useful for interactive teaching, where students predict a value before it is shown.

Extras

Scribble — a floating pad to write or sketch on. Annotate (in the Graphs window) — draw over a graph; each graph keeps its own marks.

Touch

Drag probes, meters, windows, sliders and the switch with a finger or Apple Pencil exactly as with a mouse.

Build Your Own — Help

What this tab is for

Build any arrangement of cells and capacitors and read the potential difference, charge and stored energy once the circuit has settled. In the settled state a capacitor is fully charged and no current flows, so this tab is about charge and energy rather than current. There are no resistors: they only affect how long charging takes, never the final settled state.

Building a circuit

To add a component, drag its tile from the palette onto the canvas, or on a touch screen tap the tile to highlight it and then tap the canvas to place it. Drag an endpoint to rotate or resize a component, or onto another endpoint to wire the two together — a blue dot marks where three or more ends join. Only one cell is allowed; the cell tile greys out once one is placed.

Long-press a component (or right-click on a computer) to delete it. The rest of the circuit keeps its charge, just as a real circuit would; a deleted capacitor takes its own charge away with it, and deleting the cell zeroes its delivered-energy total.

Components

Cell — the supply; set its EMF in the inspector, and press r to reverse its polarity. Capacitor — set its capacitance and, for a source-free circuit, an initial charge; press r to turn it around — a charged capacitor’s charge goes with its plates. Variable capacitor — drag the arrow on its body to change the capacitance live. Switch — tap its body to open or close it. SPDT switch — a changeover switch with three terminals; tap an arm to route the common to it (see below). Wire — a zero-resistance link.

The SPDT (changeover) switch

The SPDT switch has three terminals: a common (C) and two throws, A and B. Tap arm A to switch to A, tap arm B to switch to B, tap arm C to disconnect.

Wire the common to a capacitor, throw A to the cell and throw B to a second capacitor, and you have charge, isolate and share in one component: tap A to charge, tap C to isolate, tap B to share.

The inspector

Tap a component to select it; its editable properties appear in the Inspector panel, along with the settled voltage and charge for a capacitor. Changes take effect at once.

Meters

Voltmeter — drop it on, then drag its two probes onto the circuit to read a potential difference; the reading follows the probe polarity, so swapping the probes reverses its sign. Energy — touch its probe to a capacitor to read the energy stored in it, or to the cell to read the energy the cell has delivered. Rotate a probe by its handle to swing it clear of anything underneath, and move a meter by its body. To remove a meter, long-press it on a touch screen or right-click it on a computer.

Energy delivered

The energy the cell has delivered is the work it has done pushing charge into the circuit. It rises as capacitors charge, and falls if charge flows back into the cell — for instance when you reduce a connected capacitor’s value. Charge stranded by an open switch still counts, because it has not returned to the cell.

Display options

The options under the canvas let you choose, for the capacitance and the charge, whether to show the Value, just the Symbol, or to Hide it. In symbol mode, tapping the symbol on the circuit reveals its value — useful when you want students to predict a value first. Drag any label to reposition it.

Reset

Reset charge & energy — empties every capacitor and clears the delivered-energy total, without changing the circuit you have built.

Touch devices (iPad and Apple Pencil)

Everything works with a finger or an Apple Pencil. To add a component, tap its tile in the palette so it highlights, then tap the canvas where you want it — tap the highlighted tile again to cancel. On a computer you can instead drag a tile straight onto the canvas.

Tap a component to select it or, for a switch, to open and close it; for an SPDT switch, tap the A, B or common arm to route the common to that terminal. A small movement is ignored so a tap does not nudge anything. Drag endpoints, probes, meters, wiper arrows and labels just as with a mouse. Long-press a component to delete it.

Use Annotate to draw over the circuit and Scribble for a free notepad; rest your palm on the screen while writing with the Pencil, as touches from your hand are ignored while a pen stroke is in progress.