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

Options

A. `(5)/(2) ,(2)/(5)`
B. `(5)/(2) ,(5)/(2)`
C. `(2)/(5) ,(5)/()`
D. `(2)/(5) ,(2)/(5)`

Answer

A

Explanation

(a) Resistance `R_(2)` of `500 W` bubl ` = ((220)^(2))/(500)`
Resistance `R_(2)` of `200 W` bulb `= ((220)^(2))/(200)`
When joined in parallel, the potential difference across both the bulbs will be same.
Ratio of heat produced `= (V^(2) // R_(1))/(V^(2) // R_(2)) = (R_(2))/(R_(1)) = (5)/(2)`
When joined in series, the same current will flow through both the bulbs.
Ratio of heat produced ` = (i^(2) R_(1))/(i^(2) R_(2)) = (R_(1))/(R_(2)) = (2)/(5)`