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
Diffcult
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(a) 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}$
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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