ARCH-P-01: Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter Tables

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-01: Why the 145s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~145s (Blows 90s Clock)

First compute

\frac{1}{R_p} = \frac{1}{6} + \frac{1}{12} = \frac{18}{72}

, invert to get

R_p = 4\,\Omega

, add

R_s = 2\,\Omega

to obtain

R_{\text{tot}} = 6\,\Omega

, solve

I = \frac{12}{6} = 2.0\text{ A}

, and finally multiply

V_p = I R_p = 8.0\text{ V}

(~120s).

The Fast ShortcutTarget: 40s (Saves 105s)

Line 1 (Product-Over-Sum):

R_p = \frac{6\times 12}{6+12} = 4\,\Omega \implies R_{\text{tot}} = 2 + 4 = 6\,\Omega

.
Line 2 (Column Prune):

I = \frac{12}{6} = 2.0\text{ A}

and

V_p = 2.0\times 4 = 8.0\text{ V}

(30s).

Where Students Lose Time: In 23 past UAT-UK questions (9.87% of Physics), candidates lose 105s by using conductance 1/r_p instead of resistance r_p = (r₁*r₂)/(r₁+r₂). Instead, apply P1 with Maths 1 skill M3.4.

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