Four filament bulbs D, E, F, and G have labeled operating resistances of 2 Ω, 4 Ω, 4 Ω, and 6 Ω, respectively.
• Bulbs D and E are connected in series to form Branch 1.
• Bulb F alone forms Branch 2.
Branches 1 and 2 are connected in parallel across an ideal 12 V battery.
• Bulb G is then placed in series with the combined parallel network, so every charge that leaves the positive terminal passes through bulb G before entering the parallel section.
Assume all bulbs quickly reach the listed resistances.
(a) Determine the magnitude of the current that leaves the battery while all four bulbs are intact.
(b) Rank the bulbs from brightest to dimmest under the conditions in part (a). Clearly indicate any ties and support your ranking with quantitative reasoning.
(c) Suppose bulb E suddenly fails open (its filament breaks, leaving an open circuit). Predict how the brightness of bulbs D, F, and G changes, if at all, and justify each prediction.