A wire of resistance $$R$$ is bent in the form of a circle and is connected to a $$220\text{ V}$$ source as shown (Above, Right). If the energy provided by the source in $$42\text{ s}$$ is same as the energy required to raise the temperature of 11 kg of water through $$44^\circ\text{C}$$, find the value of $$R$$ (in ohm).
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The source is connected across points $$90^\circ$$ apart, so the arcs $$\frac{R}{4}$$ and $$\frac{3R}{4}$$ are in parallel, giving $$\frac{3R}{16}$$. The heat needed is $$11 \times 4200 \times 44 = 2032800\text{ J}$$, and the source gives $$\frac{220^2 \times 42}{3R/16} = \frac{2032800}{3R/16}$$. Equating, $$\frac{3R}{16} = 1\,\Omega$$, so $$R = \frac{16}{3} \approx 5.33\,\Omega$$.