# Circuit Dynamics Analyzer - rheostat changes, output power, fault finding

> Move a rheostat or change an LDR or thermistor and watch every meter in a circuit with internal resistance update; output power, capacitors, faults, practice.

- URL: https://qilingtools.com/en/physics/circuit-dynamics
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Pick a classic circuit with a source of EMF E and internal resistance r (R₁ in series with R₂ parallel to a rheostat, a simple series circuit, or a mixed network), drag the rheostat slider, or swap the variable element for a light-dependent resistor or thermistor and change the light or temperature. Every ammeter and voltmeter reading is solved exactly by nodal analysis and marked with ↑ or ↓, and a table checks the familiar “series opposite, parallel same” rule against the exact result. Other tabs plot output power against load, the source U–I line, capacitor charge changes, open and short-circuit fault diagnosis, and random practice.

## How to use

1. Choose a circuit and a variable element (rheostat, LDR or thermistor); set E, r and the resistors
2. Drag the slider or change light or temperature and watch each meter and its arrow; compare with the rule table
3. Add a capacitor across an element to see Q = CU and the change ΔQ
4. On Output power, drag Rv and read the three power curves and their maxima
5. Use Faults and Practice to diagnose faults or predict meter changes with instant marking

## Features

- Three classic exam circuits solved exactly by nodal analysis
- Rheostat, light-dependent resistor and NTC thermistor as the variable element
- Rule-of-thumb prediction vs exact change for every meter, with the r = 0 exception
- Output power, power in Rv and in R₀ vs Rv, maximum at R = r, the equivalent-source trick and the U–I graph
- Capacitor across an element: Q = CU, ΔQ after an adjustment and the charge released when disconnected
- Open/short fault diagnosis (indistinguishable faults both count) and random practice

## FAQ

### What is the “series opposite, parallel same” rule?

In a circuit with internal resistance, when one resistor (say a rheostat) increases, everything in series with it—everything its current flows through—gets less current, voltage and power, while everything in parallel with it, including the terminal voltage, gets more. The rheostat's own current falls but its voltage rises. The tool shows the rule's prediction and the exact result for each meter side by side.

### When does the rule fail?

It needs internal resistance (or some other series resistance to absorb the change). With r = 0 the terminal voltage always equals the EMF, so parts connected straight across the source do not change. For awkward networks the safe method is local → whole → local: R changes → R_ext → I = E/(R_ext + r) → U = E − Ir → each branch.

### When is the output power of a source greatest?

P = E²R/(R + r)² is greatest when the external resistance equals the internal resistance, giving E²/(4r) at 50% efficiency. For the largest power in a variable resistor Rv in series with R₀, treat R₀ as part of the source: Rv = R₀ + r. The power in the fixed R₀ simply grows with current, so it peaks at Rv = 0.

### How do I handle a capacitor in a DC circuit?

In steady state no current flows in the capacitor's branch, so resistors in series with it drop no voltage, and the capacitor voltage equals the voltage across whatever it is connected across; Q = CU. When an adjustment changes that voltage, the capacitor charges or discharges by ΔQ = C·ΔU. With the source removed it discharges through the resistor it is connected across.

### How can meter readings reveal a fault?

Zero current in a series circuit means an open circuit somewhere; the voltmeter that then reads almost the full source voltage spans the break. A rising current with one voltmeter dropping to zero means the part it measures is shorted. The Faults tab hides a random open or short and shows normal and faulty readings for you to diagnose.

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