Locate a fault using node and current constraints

Locate a mechanism, not a colored component

A display shows junction voltage 0 V. That does not automatically mean the circuit is open or that the source is off. Voltage compares two points: here it is junction potential minus return potential. Two points can share a potential while current flows elsewhere in the circuit. Trace the connections and ask which other reading would distinguish the candidate mechanisms.

The nominal path is source positive → R1 → junction → R2 → return, with R1 = 100 Ω and R2 = 200 Ω. The source is ideally 6 V except in the explicitly supplied weak-source case. Positive loop current follows that path. The model’s probes preserve these definitions; a negative value introduced by reversing a paper voltmeter’s leads would require a changed polarity statement, not a new fault name.

Explain a zero junction two ways

If R1 is open, no complete source-to-return path exists. Current is zero. The junction connects to return through intact R2, and the drop across that resistor is I × R2 = 0 × 200 = 0 V. Thus the junction sits at return potential. The full source difference appears across the upstream break rather than across R2.

If R2 is bypassed, an ideal wire instead holds the junction at return potential. R1 still has a complete path to the source. Current is 6/100 = 0.060 A = 60 mA. The same zero junction voltage therefore accompanies two very different currents. A current reading after the zero junction result distinguishes those two supplied explanations.

This does not mean zero resistance can be inserted into every existing solver. The bypass changes topology; its equation is derived for that path. These are virtual cases, and the illustration is not a direction to make an actual energized bypass.

Explain an open downstream component

With R2 open, the loop current is again zero. But the junction remains connected to source positive through intact R1. Its zero-current drop is 0 V, putting the junction at 6 V relative to return. A voltmeter can therefore indicate nonzero voltage across a break while no loop current flows. The ideal voltmeter draws no current, so it does not restore the loop.

Together, junction and current give these mechanism pairs: healthy 4 V, 20 mA; open R1 0 V, 0 mA; open R2 6 V, 0 mA; bypassed R2 0 V, 60 mA; weak ideal source 2 V, 10 mA. These predictions are unique within the supplied set. They are not a universal dictionary of real circuit faults.

Check a healthy result through two relationships

For the healthy circuit, current 0.020 A predicts R1’s drop as 2 V and R2’s as 4 V. Their sum is 6 V. The junction-relative-to-return reading independently constrains the lower segment’s voltage, while the current constrains the whole series path. “Independent” here refers to complementary physical constraints, not a proven statistical independence of instrument errors.

You can also check power on paper: source power is 6 × 0.020 = 0.120 W. R1 dissipates 0.020² × 100 = 0.040 W and R2 dissipates 0.080 W. Their sum closes the ideal electrical energy-rate account. This calculation does not predict resistor temperature or practical component ratings. OpenStax’s resistor treatment supplies the underlying current, voltage and power relationships; the diagnostic comparisons here are original.

Keep the evidence sequence visible

For an available case, predict junction voltage first, record it in the dedicated notebook, then predict current from the surviving mechanisms before requesting it. Retain both original predictions. If that case’s two slots were already used differently, analyze its saved pair or perform this sequence on paper; do not claim a new unexposed run. Case history and reveal exposure persist across navigation and reload.

Transfer: reverse a stated polarity

A hypothetical healthy case gives junction-minus-return = +4 V. On paper, reverse the voltmeter leads while leaving the circuit and current reference unchanged. Predict the new voltage and explain whether the current must reverse.

Check the polarity transfer

The voltmeter now reports return-minus-junction = −4 V. The physical circuit is unchanged, so the positive conventional loop current remains 20 mA under the original reference. A sign change caused by the measurement definition is not evidence of a reversed source or a new fault. Reversed leads are a paper extension, not an extra widget control.

Return to circuit power for the energy-rate check, or continue to diagnosis limits before generalizing from a successful finite-case match.