Simulating circuit measurements safely

A low-voltage circuit simulator obeys Kirchhoff's rules, so measurements in it follow the same rules as in a real laboratory: an ammeter is connected in series with a component, and a voltmeter is connected in parallel with it. An ammeter has a very small internal resistance $R_A \approx 0$, and if it is mistakenly connected in parallel with the source, it creates a near short circuit through which a huge current can flow, $I = \frac{U}{R_A + r}$. In the simulator this is safe: you will see an abnormally large current or an error message, whereas in real hardware it would cause overheating, sparking, or a blown fuse. Before every measurement, check the instrument mode, the range, and the connection point, and make sure a load resistor is present in the loop. By comparing simulator readings with calculations based on Kirchhoff's rules for series and parallel sections, you check both the circuit and your own measurement procedure.

A series circuit is built in the simulator: source $U = 9\ \text{V}$, $R_1 = 100\ \Omega$, $R_2 = 200\ \Omega$. Where should the ammeter be placed to measure the current through $R_2$, and where should the voltmeter be placed to measure the voltage across $R_2$? Compute the expected readings.

A parallel circuit: source $U = 6\ \text{V}$, $R_1 = 100\ \Omega$, $R_2 = 300\ \Omega$. One ammeter measures the total current and a second one measures the current through $R_1$. Compute both currents, check Kirchhoff's current rule, and state where to place a voltmeter.

In the simulator, an ammeter (ideal, $R_A = 0$) was connected directly across the terminals of a source $U = 9\ \text{V}$. The simulator reports an error or an abnormally large current. Explain the cause, estimate the current for real instruments ($R_A = 0.1\ \Omega$, source internal resistance $r = 0.5\ \Omega$), and propose a safe measurement circuit with a load $R = 100\ \Omega$.

Self-study plan in a simulator (for example, PhET “Circuit Construction Kit”, DC mode). No real measurements are performed — every action is safe.

1. Build a series circuit: source $9\ \text{V}$, $R_1 = 100\ \Omega$, $R_2 = 200\ \Omega$.
2. Calculate the expected $I$ and $U_2$ from Kirchhoff's rules, then measure them in the simulator (ammeter in series, voltmeter in parallel).
3. Compare the values using $\frac{|X_{\text{sim}}-X_{\text{calc}}|}{X_{\text{calc}}}\cdot 100\%$ and record the difference.
4. Replace the circuit with a parallel one: $6\ \text{V}$, $R_1 = 100\ \Omega$, $R_2 = 300\ \Omega$; measure the total current and one branch current, and verify $I = I_1 + I_2$.
5. A deliberate mistake in a safe environment: connect the ammeter directly in parallel with the source and note the simulator's response.
6. Fix the circuit (ammeter in the break, in series with a load) and explain in two or three sentences why this mistake on real hardware would blow a fuse or damage the instrument.

To show the difference between correct and hazardous instrument connections and to let the learner predict readings from the schematic in advance.

A two-panel schematic. Left panel (correct): a source $U$ with an ammeter $A$ in series (symbol $A$ in a break in the loop), resistors $R_1$ and $R_2$; a voltmeter $V$ drawn in parallel with $R_2$; labels with expected values such as $I = 30\ \text{mA}$, $U_2 = 6\ \text{V}$. Right panel (hazardous): the same source, but the ammeter $A$ is connected in parallel with the terminals; the low-resistance loop is highlighted with a thick red line, an arrow, and a warning symbol, next to the formula $I = \frac{U}{R_A + r}$ and the label “short circuit”. Both panels are captioned “ammeter in series, voltmeter in parallel”.

In a simulator, we build a circuit: $5.0\,\text{V}$ source, cable resistance $0.2\,\Omega$, phone equivalent $5.0\,\Omega$. We connect the ammeter in series and the voltmeter in parallel with the load. Expected current $I = 5.0/(5.0+0.2)=0.96\,\text{A}$; cable drop $U = 0.96 \cdot 0.2 = 0.19\,\text{V}$. If we mix up the mode and put the ammeter in parallel with the source, the simulator shows a fault current, but nothing burns.

This exercises safe placement of the ammeter in series and the voltmeter in parallel, range selection, and polarity checks; it uses Ohm's law for a series circuit with wire losses.

In a simulator: $9.0\,\text{V}$ battery, $330\,\Omega$ resistor, LED with forward drop $2.0\,\text{V}$. We connect the ammeter on the $200\,\text{mA}$ range in series. Current $I=(9.0-2.0)/330=0.0212\,\text{A}=21.2\,\text{mA}$. A voltmeter in parallel with the resistor reads $U_R=0.0212\cdot 330=7.0\,\text{V}$. We check that the polarity of the LED and ammeter is not reversed.

This scenario trains safe selection of multimeter mode and range, series connection of the ammeter and parallel connection of the voltmeter, and polarity checks; the calculation relies on a series circuit and Ohm's law.

In a simulator: $12.6\,\text{V}$ battery, two sockets in parallel, each device $6.0\,\Omega$. Branch: $I_1=I_2=12.6/6.0=2.1\,\text{A}$; total current $I=4.2\,\text{A}$; fuse $5\,\text{A}$. We connect an ammeter on the $10\,\text{A}$ range in the common branch, then in each branch in turn. A voltmeter in parallel with each load reads $12.6\,\text{V}$. If the ammeter is placed in parallel with the battery, the simulator shows a short circuit and the fuse blowing.

This practices safe measurement of branch currents and total current, selection of the $10\,\text{A}$ range, and the prohibition on connecting an ammeter in parallel with the source; it uses Kirchhoff's current rule and parallel connection.