Three identical resistive light bulbs—labeled A, B, and C—are connected to an ideal 12V battery in an arrangement that is hidden from view. The bulbs are known to be connected using only series and/or parallel combinations, but the exact configuration is unknown to you.
You are able to make the following measurements without disturbing the hidden wiring:
• An ideal ammeter placed in series with the entire network reads 2.0A.
• An ideal voltmeter connected directly across bulb A alone reads 4.0V.
No other measurements are possible.
(1) Part 1: (a) Using the readings given, calculate the equivalent resistance of the entire hidden network.
(2) Part 2: (b) Determine the current through bulb A.
(3) Part 3: (c) Considering all simple series/parallel configurations that could be built with three identical resistors, use the results of parts (a) and (b) to deduce the specific arrangement of the bulbs. Fully justify your reasoning.
(4) Part 4: (d) For the configuration you identified in part (c), calculate the current through each bulb and the power dissipated by each bulb.