• # question_answer Two bulbs of 500 watt and 200 watt are manufactured to operate on 220 volt line. The ratio of heat produced in 500 W and 200 W, in two cases, when firstly they are joined in parallel and secondly in series, will be [MP PET 1996; DPMT 1999] A)            $\frac{5}{2},\,\frac{2}{5}$     B)            $\frac{5}{2},\,\frac{5}{2}$ C)            $\frac{2}{5},\,\frac{5}{2}$     D)            $\frac{2}{5},\,\frac{2}{5}$

Correct Answer: A

Solution :

Resistance ${{R}_{1}}$ of  500 W bulb $=\frac{{{(220)}^{2}}}{500}$ Resistance ${{R}_{2}}$ of  200 W bulb $=\frac{{{(220)}^{2}}}{200}$ When joined in parallel, the potential difference across both the bulbs will be same. Ratio of heat produced $=\frac{{{V}^{2}}/{{R}_{1}}}{{{V}^{2}}/{{R}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{5}{2}$ When joined in series, the same current will flow through both the bulbs. Ratio of heat produced $=\frac{{{i}^{2}}{{R}_{1}}}{{{i}^{2}}{{R}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{2}{5}$

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