Hanging the Voltmeter — Potential Difference by Kirchhoff
A slate circuit board on a lab bench carries two sealed lead-acid batteries, eight gold power resistors and an LED ammeter, wired as two loops plus a pair of parallel paths that meet at the point Y — and Y is joined to an earth terminal by a green-yellow lead. A handheld multimeter lies on the bench with its two probe pens. Sliders set both batteries and two of the resistors, and the circuit is solved exactly the moment anything changes. Press ▶: with the probes on A and B, a test charge walks from A to B the long way round under a potential fence; then the probes move to X and to the earth terminal, and a second walk goes from Y out to X. The walks play once and stop, and the timeline takes you back to any moment.
इस सिमुलेशन का उपयोग कैसे करें
- Front battery (V_B)₁ — 0 to 40 V, starting at 30 V.
- Back battery (V_B)₂ — 0 to 40 V, starting at 20 V.
- Middle resistor R_mid — 1 to 20 Ω, starting at 10 Ω.
- Left resistor R_left — 1 to 30 Ω, starting at 12 Ω. Every change re-solves the circuit 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.
क्या देखें
- At the starting values the multimeter reads 0.800 V between A and B, and the ammeter reads −0.800 A: the current through it runs against its printed arrow.
- Follow walk 1: the fence rises 0.80 V from A to Y through the 2 Ω, then falls 1.60 V from Y to B through the 8 Ω — the meter's 0.80 V is exactly what brings it back to A.
- In walk 2 the fence climbs 5.60 V through the 7 Ω, walking against the current, then drops 30 V inside the battery and gets 0.80 V back from its 1 Ω: X ends 26 V below the earth.
- Set the back battery to 0 V and the front one to 40 V: the current in the parallel paths reverses, their arrows flip, and A sits lower than B.
- Whatever the sliders, V_AB is 4/3 of I₂ (in volts per ampere): it depends only on the current that enters the two parallel paths.
इसके पीछे की भौतिकी
Once Kirchhoff's laws have given every current, the potential difference between any two points follows from the loop rule. Hang a voltmeter between the two points and treat its reading as one more term of a loop that runs through the circuit from one probe to the other and comes back through the meter: all the rises and falls round that loop must cancel. With the 30 V and 20 V batteries (each with 1 Ω inside) the currents are I₁ = −0.8 A — the ammeter reads against its printed arrow — I₂ = 0.6 A and I₃ = 1.4 A. In the two parallel paths I₂ splits in inverse proportion to their resistances: 0.4 A through the 6 Ω path and 0.2 A through the 12 Ω path. Walking from A through the 2 Ω against its 0.4 A raises the potential by 0.8 V; walking on from Y through the 8 Ω with its 0.2 A lowers it by 1.6 V. Coming back to A through the meter must undo the net −0.8 V, so 0 = 0.4 × 2 + V_AB − 0.2 × 8 and V_AB = 0.8 V. The potential of a point is its potential difference from the earth, which is taken as zero: with the black probe on the earth terminal the meter reads V_X itself. Walking from Y through the 8 Ω and 4 Ω with the current, through the 7 Ω against it, and through the 30 V battery from + to −, gives −30 = V_XY + 0.2 × (8 + 4) − 0.8 × (7 + 1), so V_X = −26 V. The route does not matter: every route between the same two points gives the same answer, because every closed loop adds up to zero.