First slide

Electrical power

Question

Assuming all bulbs are identical, rank the brightnesses of the bulbs, from brightest to dimmest.

Moderate

A

A > D - H > B - C > E - F = G
B

A > B - C > D - H > E - F = G
C

A > D - H > E - F - G > B = C
D

All have equal brightness

Solution

For the branch containing A, B and C.
$R_{e q} = \frac{3 R}{2}$
Current in A : $I_{1} = \frac{E}{R_{eq}} = \frac{2 E}{3 R}$
Current in each of B and C = ${I^{'}}_{1} = \frac{I_{1}}{2} = \frac{E}{3 R}$
For the branch containing D, E, F, G and H:
$R_{e q} = \frac{7 R}{3}$
Current through D and H: $I_{2} = \frac{3 E}{7 R}$
Current through each of E, F and G:
${I^{'}}_{1} = \frac{I_{2}}{3} = \frac{E}{7 R} Since I_{1} > I_{2} > {I^{'}}_{1} > I^{'}$
A > D = H > B = C > E = F = G

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