Question

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

• 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

Answer 1

Answer: (A)

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 $C: I_{1}^{\prime}=\frac{I_{1}}{2}=\frac{E}{3 R}$
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_{2}^{\prime}=\frac{I_{2}}{3}=\frac{E}{7 R} \text { Since } I_{1} > I_{2} > I_{1}' > I_{2}' $
$A > D= H > B=C > E= F=G$