Question

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

• A. $\frac{5}{2},\frac{2}{5}$
• B. $\frac{5}{2},\frac{5}{2}$
• C. $\frac{2}{5},\frac{5}{2}$
• D. $\frac{2}{5},\frac{2}{5}$

Answer 1

Answer: (A)

$\frac{5}{2},\frac{2}{5}$

Answer 2

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 $= \frac{i^{2}R_{1}}{i^{2}R_{2}} = \frac{R_{1}}{R_{2}} = \frac{2}{5}$