Question

A 100 W bulb $B_1$ and two 60 W bulbs $B_2$ and $B_3$ are connected to a 250 V source as shown in figure. $W_1$, $W_2$and $W_3$are the output powers of the bulbs $B_1$, $B_2$ and $B_3$ respectively then

• A. W₁ > W₂ = W₃
• B. W₁ > W₂ > W₃
• C. W₁ < W₂ = W₃
• D. W₁ < W₂ < W₃

Answer 1

The correct option is D W₁ < W₂ < W₃

The resistances of bulbs $B_1,B_2$ and $B_3$ respectively are
$R_1\frac{v^2}{w_1}=\frac{(250{)}^2}{100}=625$ ohm
$R_2=\frac{(250{)}^2}{60}=1042$ ohm =$R_3$
Voltage across $B_3$ is $V_3=250V$
Voltage across $B_1$ is $V_1=\frac{V{R}_1}{(R_1+R_2)}=\frac{250\times 625}{(625+1042)}=93.7V$
Voltage across $B_2$ is $V_2=250-93.7=156.3V$
Power output $W_1=\frac{V^2}{R_1}=\frac{(93.7{)}^2}{625}=14W$
$W_2=\frac{(156.3{)}^2}{1042}=23w$
$W_3=\frac{(250{)}^2}{1042}=60w$
Hence $W_1<W_2<W_3$