Question

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

• A. all have equal brightness
• B. $A>B=C>D=H>E=F=G$
• C. $A>D=H>E=F=G>B=C$
• D. $A>D=H>B=C>E=F=G$

Answer 1

The correct option is D $A>D=H>B=C>E=F=G$

Brightness of the bulb $\propto$ current through the bulb
Let the resistance of each bulb be $R$
For the branch containing bulbs $A,B,C$
$R_{eq}=R+\left[\frac{R\times R}{R+R}\right]$
$=R+\frac{R}{2}=\frac{3R}{2}$
$i=\frac{2E}{3R}$
Current through $A=\frac{2E}{3R}$
Current through $B$ and $C$ $A=\frac{1}{2}\left[\frac{2E}{3R}\right]$
$=\frac{E}{3R}$
For the branch containing $D,E,F,G$ and $H$
$R_{eq}=R+\frac{R}{3}+R=\frac{7R}{3}$
$i=\frac{3E}{7R}$
Current through $D$ and $H=\frac{3E}{7R}$
Current through $E,F,G=\frac{1}{3}\left(\frac{3E}{7R}\right)=\frac{E}{7R}$
Hence the bulbs from brightest to dimmest can be arranged as
$A>D=H>B=C>E=F=G$
Hence, option $\left(a\right)$ is correct.