Walking Out from the Earth — the Potential of Three Points
A slate circuit board on a lab bench carries three arms of a larger circuit that meet at the post Y, and a green-yellow lead with an ammeter in it joins Y to an earth terminal. Each arm holds two sealed lead-acid batteries and two gold power resistors, with a brass post between every two parts. A multimeter lies on the bench in front: its black crocodile clip grips the earth terminal and its red probe pen can touch any post. Three sliders set the current in each arm. Press ▶: a test charge walks out from Y along arm X, then arm K, then arm Z, under a potential fence, and after each part the red probe hops onto the next post so the meter reads that post's potential. The walks play once and stop, and the timeline takes you back to any moment.
Cara memakai simulasi ini
- Arm X current I_X — 0 to 10 A, starting at 8 A, flowing from Y towards X.
- Arm K current I_K — 0 to 10 A, starting at 6 A, flowing from K towards Y.
- Arm Z current I_Z — 0 to 10 A, starting at 2 A, flowing from Z towards Y. Every change re-computes all the potentials and keeps the moment on screen; nothing moves until you press ▶.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion.
- Drag anywhere on the scene to look around.
Yang perlu diamati
- Along arm X the meter reads −10 V after the 6 V battery and its 2 Ω, −42 V after the first 4 Ω, −62 V after the 12 V battery and its 1 Ω, and −94 V at X.
- Along arm K every resistance raises the potential, because the walk goes against the current: 36 V, 42 V, 42 V and finally 78 V at K.
- Arm Z dips to −11 V inside the 14 V battery, yet ends at +3 V: its 9.5 Ω, walked against 2 A, give back 19 V.
- Set all three currents to zero: the ends sit at −6 V, 24 V and −16 V — the batteries' voltages alone.
- Raise I_X to 10 A: 2 A must now come up from the earth into Y, and the ammeter in the earth lead reads −2.000 A.
Fisika di baliknya
The earth is the zero of potential, so the potential of a point is its potential difference from the earth — what a voltmeter reads with its black lead earthed. Here Y is earthed, and walking out from Y along an arm the potential changes part by part: through a battery from − to + it rises by V_B, from + to − it falls by V_B; through a resistance — each battery's internal resistance included — it falls by IR when the walk goes with the current and rises by IR when it goes against it. Arm X carries 8 A outward, the same way as the walk: V_X = 0 + 6 − 8 × 2 − 8 × 4 − 12 − 8 × 1 − 8 × 4 = −94 V. Arm K carries 6 A towards Y, against the walk: V_K = 36 + 6 × 1 − 12 + 6 × 2 + 6 × 6 = 78 V. Arm Z carries 2 A towards Y and crosses both its batteries from + to −: V_Z = −2 + 2 × 0.5 + 2 × 2 − 14 + 2 × 1 + 2 × 6 = 3 V. Written as a loop that comes back to Y through the voltmeter, ΣV_B = ΣIR becomes 6 − 12 = V_XY + 8 × (4 + 4 + 1 + 2), 36 − 12 = V_KY − 6 × (6 + 2 + 1) and −14 − 2 = V_ZY − 2 × (6 + 1 + 2 + 0.5). Each end potential is its batteries' share plus a part proportional to the arm's current, so doubling a current doubles only that IR part. Where the arms meet, the junction rule settles the earth lead: I_K + I_Z − I_X flows into the earth — exactly zero for 8 A, 6 A and 2 A.