An electric kettle has two windings. When one of them is switched on, the water in the kettle begins to boil in 15 minutes, and when the other is switched on it takes 30 minutes for water to boil. If

Question

An electric kettle has two windings. When one of them is switched on, the water in the kettle begins to boil in 15 minutes, and when the other is switched on it takes 30 minutes for water to boil. If the two windings are joined in series and switched on, water in the kettle begins to boil in 4 α hr. Assuming no heat loss to the surrounding, find the value of α .

TestHub · Accepted Answer

Let the resistance of winding 1 and 2 be $R_{1}$ and $R_{2}$ , respectively.

Therefore, when winding 1 is present, $P = \frac{V ^{2}}{R}$ .

Thus, $m_{w a t er} L_{f} = \frac{V ^{2}}{R _{1}} \times 15 \dots (i)$

For the second winding,

$P = \frac{2 2 ^{2}}{R}$

$m_{w a t er} L_{f} = \frac{2 2 ^{2}}{R} t (ii)$

When the windings are joined in series,

$R_{e q} = R_{1} + R_{2} = 2 R$

$P = \frac{21 2 ^{2}}{2 R}$

$m_{w a t er} L_{f} = \frac{21 2 ^{2}}{2 R} t (iii)$

From equations (i), (ii), and (iii),

$t = 45 min$

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