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# Two bulbs consume same power when operated at $200V\: and\: 300V$ respectively. When these bulbs are connected in series across a $DC$ supply of $500V$, then consider the following statements

$\begin {array} {1 1} (1)\;\text{Ratio of potential difference across them is} \large\frac{3}{2}\\(2)\;\text{Ratio of potential difference across them is} \large\frac{4}{9} \\ (3)\;\text{Ratio of power consumed across them is } \large\frac{4}{9}\\ (4)\;\text{Ratio of power consumed across them is} \large\frac{3}{2} \end {array}$

Which of the above statements are true:

$\begin {array} {1 1} (A)\;1\: and \: 3 & \quad (B)\;1\: and \: 4 \\ (C)\;2\: and \: 3 & \quad (D)\;2\: and \: 4 \end {array}$

In the first case when both bulbs consume same powerwhen operated at 200V and 300V respectively, we have
When connected in series, the potential drop is in the ratio of the resistances
$P = \large\frac{V_1 ^ 2}{R_1} = \frac{V_2 ^ 2}{R_2}$
$\large\frac{R_1}{R_2} =\frac{ V_1 ^ 2}{V_2 ^ 2}$
$\qquad =\large\frac{4}{9}$
Ans : (C)
edited Sep 11, 2014 by meena.p