Ohm’s law for a complete circuit and EMF

Equipment

• Source with emf ℰ and internal resistance r (3D model, drag to rotate)
• Slider “Cảm ứng từ / mức” (tesla readout, sets the plot amplitude)
• Slider “Góc / tốc độ” (acts as internal resistance r in the readout, Ω)
• “Tạm dừng / Chạy tiếp” button on each figure
• Current readout “I = ℰ/(R+r)” (A)

Procedure

1. Read the complete-circuit current

   In section 1, observe the source model and the loop; drag the canvas to rotate the view. Read the line “I = ℰ/(R+r) = … A (ℰ = 1 V, R = 1 Ω, r = … Ω)” and check it against $I = \frac{\mathcal E}{R+r}$ computed from the displayed numbers.

2. Vary the internal resistance r

   Move the “Góc / tốc độ” slider from low to high — it controls r (Ω) in the readout. Record I at three values of r and check that I decreases as r rises, following $I = \mathcal E/(R+r)$; as r → 0 the source becomes ideal and $U \to \mathcal E$. Press “Tạm dừng” if you want the figure frozen while reading.

3. Compare with the quantitative graph

   In section 2 the graph updates with the parameters; hold one slider fixed and vary the other. Use “Cảm ứng từ / mức” to change the displayed amplitude and “Góc / tốc độ” to change r; re-read the section-2 readout and check the terminal voltage with $U = \mathcal E - Ir$ for each pair (I, r).

4. Predict the ideal-source limit

   Before dragging “Góc / tốc độ” to its minimum, predict I and U for r ≈ 0 using $I \approx \mathcal E/R$ and $U \approx \mathcal E$; then move the slider to check. Conversely, set r to maximum and note the weak current — explain why an old battery (large r) still measures an open-circuit voltage near $\mathcal E$ yet delivers current poorly.

Simulation

Experiment history

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