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UAT-UK SPEC: P1MODULE: PHYSICSTOPIC ID: ARCH-P-01

Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter Tables

Master Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter Tables on the ESAT Physics paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 40s, saving +105s per question.

Standard Classroom Time
145s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
40s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+105s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Product-Over-Sum): Rp=6×126+12=4 Ω  ⟹  Rtot=2+4=6 ΩR_p = \frac{6\times 12}{6+12} = 4\,\Omega \implies R_{\text{tot}} = 2 + 4 = 6\,\Omega.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Column Prune): I=126=2.0 AI = \frac{12}{6} = 2.0\text{ A} and Vp=2.0×4=8.0 VV_p = 2.0\times 4 = 8.0\text{ V} (30s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1intermediate_stop_trap

Forgetting to invert 1/Rₚ = 1/R₁ + 1/R₂, adding 1/Rₚ directly to R(series)

Using conductance 1/Rₚ instead of resistance Rₚ = (R₁*R₂)/(R₁+R₂).

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2sign_or_direction_flip

Assuming voltmeter across variable resistor R(var) decreases when R(var) increases

Confusing current decrease (I drops) with potential divider share V(var) = V(in) * R(var)/(R(fixed) + R(var)) (which rises).

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3table_column_pruning_trap

Evaluating complex branch voltages before checking total circuit current ammeter column first

Failing to prune 50% of table rows immediately via total resistance -> main ammeter trend.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter Tables

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Full Lesson All 15 Questions (ARCH-P-01)
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ARCH-P-01: Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter Tables (Sample)Physics
00:00.0
SUB-90 ZONE (<35S)
0.0s35s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-P-01 (6-Card Lesson)Format: Table-Row Matching
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Question 1 of 1 • 90s Target

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