DC Circuits and Signal Math
Calculate and measure DC voltages, graph dynamic signals, and wield differential equations and complex phasors to decode circuit behavior.
Like Duolingo, but for DC Circuits and Signal Math. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 10 levels across 2 sections, about 20 minutes end to end, roughly 4 days at five minutes a day. It moves through Measuring DC and Sketching Waveforms and Predicting Circuit Transients and AC States. It starts from scratch.
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Key ideas in DC Circuits and Signal Math
- Voltage acts as the electrical push while resistance opposes the flow of charge
- Higher resistance under a fixed voltage restricts the flow, causing current to drop proportionally (I = V/R)
- Ohm's law governs the direct relationship between voltage drop, current, and resistance
- Current cannot build up or disappear at an electrical junction
- Total current entering a node must equal total current leaving it (Kirchhoff's Current Law)
- Subtracting exiting currents from entering currents gives the balance flowing through remaining branches
- Tracing any complete closed path in a circuit returns to the starting potential energy (Kirchhoff's Voltage Law)
- Energy provided by sources equals energy lost across resistive elements in a closed loop
- The algebraic sum of voltage rises and drops around any closed loop is zero
- Series components share the exact same current
- Two resistors in series split the total source voltage in direct proportion to their resistance values
- Equal resistors in series split the applied voltage exactly in half, creating a stable midway reference voltage
- Voltage is a difference between two nodes, so a voltmeter connects in parallel across components without opening the circuit
- Current is a through-rate, so an ammeter must be inserted in series directly into the path by breaking the circuit
- Connecting an ammeter in parallel acts like a short circuit and can blow a fuse
- A step function u(t) is 0 before t = 0 and 1 after t = 0
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives DC Circuits and Signal Math the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
You keep a 9V battery hooked up, but swap your resistor for one with ten times the resistance. What happens to the current?
Get it right to open this lesson and 9 more in the app.
Where DC Circuits and Signal Math takes you
- 1
Measuring DC and Sketching Waveforms
- Analyzing and Probing DC Networks
- Visualizing Signals and Circuit Clocks
- 2
Predicting Circuit Transients and AC States
- Solving First-Order Circuit Transients
- Representing Signals with Complex Phasors
2 sections · 4 units · 10 levels. Built to play, not to enroll.
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Add Tomo to ChatGPT- What to ask
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- What you get
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You pick the voice
DC Circuits and Signal Math is taught in the Bestie style: your friend who just gets it. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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