Circuit Teaching Guide

Conceptual Foundations

Ohm's Law

$I = \frac{U}{R}$

Conditions: purely resistive circuits at constant temperature.

Ohm's Law for a Closed Circuit

$I = \frac{E}{R + r},\quad U_{\text{terminal}} = E - Ir$

Series and Parallel

Electric Power

$P = UI = I^2R = \frac{U^2}{R}$

RC Charging and Discharging

$\tau = RC,\quad U_C(t) = E(1 - e^{-t/\tau})$

The process is essentially complete after $5\tau$ (99.3%).

---

Using the Builder

Open the circuit builder (nav bar → Builder → Circuit). Components are placed on the grid canvas: pick one in the component library on the left, then drag out its two terminals on the canvas to place it - terminals landing on the same cell join into one node automatically, with no separate wiring; to change a connection, just drag a component's terminal. The circuit works only once it forms a closed loop containing a source (while it is open, the "Check for issues" panel on the right says so).

Gestures

A one-line gesture hint always sits in the bottom-right corner of the canvas; glance at it whenever an operation slips your mind.

---

Detailed Component Reference

Power Sources

EMF source (emf_source)

A real source model with an EMF and an internal resistance.

Note:

• With $r = 0$ it is an ideal source: the terminal voltage always equals $E$
• Short-circuit current $I_{\text{short}} = E/r$ - the smaller the internal resistance, the more dangerous a short circuit
• Sources in series: total $E = E_1 + E_2$, total $r = r_1 + r_2$

Constant-current source (current_source)

Delivers a constant current, unaffected by the load.

Used for: special analysis problems; rarely seen in practice.

---

Resistors

Fixed resistor (resistor)

The most basic circuit component.

Note: if resistance is set to 0, the system computes it from $\rho L/S$ (used in the resistance-of-a-wire measurement experiment).

Resistance box (resistance_box)

Integer-step resistance values, emulating a laboratory resistance box.

Rheostat (rheostat)

A continuously adjustable resistor.

Note:

• The resistance actually in the circuit = maxResistance × wiper
• Exceeding the rated current burns it out (the simulation issues a warning)
• Two hook-ups: current limiting (in series) or potential divider (all three terminals connected)

Thermistor / photoresistor (controlled_resistor)

A resistor whose value is set externally; simulates sensors.

---

Loads

Lamp (lamp)

A nonlinear load whose brightness changes visibly.

Note:

• The resistance follows from the ratings: $R = U_N^2 / P_N$
• With nonlinear=1 the cold resistance is small and the hot resistance large (the I-V curve bends)
• Actual voltage > rated voltage → over-bright / burn-out warning

Motor (motor)

A non-purely-resistive load with back EMF.

Physics: $I = \frac{U - E'}{R_L}$, input power $P_{\text{in}} = UI$, heating power $P_{\text{heat}} = I^2 R_L$, mechanical power $P_{\text{mech}} = E'I$.

Note: when the motor is stalled, $E' = 0$ and the current $I = U/R_L$ is enormous (stall current).

---

Energy-Storage Elements

Capacitor (capacitor)

Note:

• In DC steady state a capacitor is an open circuit ($I_C = 0$)
• Transient currents appear only in charge/discharge analysis
• With initialVoltage > 0 the capacitor discharges as soon as the circuit is closed

Inductor (inductor)

Note:

• In DC steady state an inductor is a short circuit ($U_L = 0$)
• Switching off produces a high voltage (self-induced EMF); the larger $L$, the more pronounced
• Time constant $\tau = L/R$

---

Measuring Instruments

Ammeter (ammeter)

Note: must be connected in series. With internal resistance = 0 it leaves the circuit undisturbed; with internal resistance > 0 it slightly reduces the current.

Voltmeter (voltmeter)

Note: must be connected in parallel across the component under test. Keeping the default internal resistance of 0 gives an ideal voltmeter (no shunting, no effect on the circuit); only set a finite value (e.g. 3000 Ω) when examining how the voltmeter's own resistance affects the measurement (the "treat the voltmeter as a large resistor" type of problem).

Multimeter (multimeter)

Galvanometer / meter movement (galvanometer)

Used for: meter-modification experiments. A small resistor in parallel → converted into an ammeter; a large resistor in series → converted into a voltmeter.

---

Control Elements

Switch (switch)

Single-pole double-throw switch (spdt_switch)

Used for: charge/discharge switch-over (throw 1 connects the source to charge, throw 2 connects the resistor to discharge).

Fuse (fuse)

Diode (diode)

Note: conducts forward (anode potential > cathode) and blocks in reverse. Connected backwards, it carries zero current.

---

Auxiliary Elements

Wire (wire)

No parameters. Joins two terminals; an ideal wire has zero resistance.

Alarm / threshold (alarm)

---

Using the Lab

Click "Run it" in the top toolbar to enter the lab (it runs the current canvas directly, no need to save first):

• DC analysis: shows each branch current (arrow + value), every component's voltage and power
• Charge/discharge analysis: plots the $U_C$-$t$ and $I$-$t$ curves in real time
• Show potentials: wires are coloured by potential (red = high, blue = low)
• Current animation: moving dots indicate the current direction
• Parameter sweep: vary one component's parameter and watch the current/voltage/power change

---

Common Problems and Cautions

• The circuit doesn't work: a closed loop is required. Check for unconnected terminals (hollow dots).
• Short circuit: a wire straight between the source's + and − terminals (no load) → enormous current; the simulation issues a red warning.
• Meter hook-up: ammeter in series, voltmeter in parallel. Reversing them changes the circuit or gives wrong readings.
• Capacitor in steady state: in DC analysis the capacitor branch carries zero current (open circuit). To watch the charge/discharge process you must select the Charge/discharge analysis mode.
• Reference direction: a negative current means the actual direction is opposite to the labelled one - not an error.
• Voltmeter internal resistance = 0: this means an ideal voltmeter (the shorthand for infinite internal resistance), not a short circuit.
• Ground reference: the ground symbol (0 V) must touch a component terminal (directly or through a wire) for the reference to sit where you put it; if it floats, the engine automatically takes the negative terminal of the first source as 0 V (the builder's "Check for issues" panel warns you).

Teaching Suggestions

• Verifying Ohm's law: source + fixed resistor + ammeter + voltmeter; vary the source voltage and record the data.
• Measuring EMF and internal resistance: vary the rheostat, record several $(I, U)$ pairs, plot the $U$-$I$ graph.
• RC charging and discharging: source + resistor + capacitor + single-pole double-throw switch; throw 1 charges, throw 2 discharges.
• Modifying a meter: put a resistor in parallel/series with a meter movement and verify the range-extension formulas.
• Motor power: observe the energy split $P_{\text{in}} = P_{\text{heat}} + P_{\text{mech}}$.

Related Experiments

• Verifying Ohm's law: $I \propto U$, $I \propto 1/R$
• Measuring resistance with the voltmeter-ammeter method: compare the errors of the internal and external connections
• Measuring a source's EMF and internal resistance: the $U = E - Ir$ graph method
• RC charging and discharging: verify the exponential law, measure $\tau$
• The lamp's I-V characteristic: nonlinear $U$-$I$ curve
• Series and parallel circuits: verify the voltage-divider and current-divider rules