Question

If $X,Y$ and $Z$ in figure are identical lamps, which of the following changes to the brightness of the lamps occur when switch $S$ is closed?

• A. $X$ stays the same, $Y$ decreases
• B. $X$ increases, $Y$ stays the same
• C. $X$ increases, $Y$ decreases
• D. $X$ decreases, $Y$ increases

Answer 1

The correct option is C $X$ increases, $Y$ decreases

Let the resistance of each bulb be $R.$
When switch is open,
$R_{eq}=R+R=2R$
$\Rightarrow I=\frac{V}{2R}$ and
Power flowing through $X$ and $Y$ is same $=P=I^{2}R=\frac{V^2}{4R}...\left(1\right)$

$R_{eq}=\frac{R}{2}+R=\frac{3R}{2}$
$I=\frac{V^2}{\frac{2R}{2}}=\frac{2V^2}{3R}$
$\Rightarrow P_X=I^{2}R=\frac{4V^2}{9R}\dots \left(2\right)$
And current flowing through $Y,I_Y=\frac{V}{2\left(\frac{2R}{2}\right)}$
$I_Y=\frac{V}{3R}$ [Since bulb $Y$ and $Z$ are identical]
$\Rightarrow P_Y=I_Y^{2}R=\frac{V^2}{9R}\dots \left(3\right)$
Comparing $\left(1\right),$ $\left(2\right),$ $\left(3\right)$ we conclude
$P_X>P$ and $P>P_Y$
$\Rightarrow$Brightness of bulb $X$ increases and $Y$ decreases.
Hence, option $\left(b\right)$ is correct.