A heater coil is cut in two parts and only one of them is used in the heater. What is the ratio of the heat produced by this half coil to that by the original coil if the voltage applied is the same?
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For same p.d. the heat produced per second,
$\text{H}=\frac{\text{V}^2}{\text{R}}\propto\frac{1}{\text{R}}.$
As the one part of heater coil has resistance $\text{R}_2=\frac{\text{R}}{2}$ being the resistance of original coil; therefore the ratio of heat produced,
$\frac{\text{H}_2}{\text{H}_1}=\frac{\text{R}_1}{\text{R}_2}=\frac{\text{R}}{\frac{\text{R}}{2}}=2:1$
$\text{H}=\frac{\text{V}^2}{\text{R}}\propto\frac{1}{\text{R}}.$
As the one part of heater coil has resistance $\text{R}_2=\frac{\text{R}}{2}$ being the resistance of original coil; therefore the ratio of heat produced,
$\frac{\text{H}_2}{\text{H}_1}=\frac{\text{R}_1}{\text{R}_2}=\frac{\text{R}}{\frac{\text{R}}{2}}=2:1$
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