a
(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 \( = \frac{{{i^2}{R_1}}}{{{i^2}{R_2}}} = \frac{{{R_1}}}{{{R_2}}} = \frac{2}{5}\)