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 $C$.
$R_{eq}=\frac{3R}{2}$
Current in $A:I_1=\frac{E}{R_{eq}}=\frac{2E}{3R}$
Current in each of $B$ and $C:I_1^{\prime }=\frac{I_1}{2}=\frac{E}{3R}$
For the branch containing $D,E,F,G$ and $H:$
$R_{eq}=\frac{7R}{3}$
Current through $D$ and $H:I_2=\frac{3E}{7R}$
Current through each of $E,F$ and $G:$
$I_2^{\prime }=\frac{I_2}{3}=\frac{E}{7R}\text{ Since }{I}_1>I_2>I_1^{\prime }>I_2^{\prime }$
$A>D=H>B=C>E=F=G$