Two heated wires of the same dimensions are first connected in series and then in parallel to a source of supply. What will be the ratio of heat produced in the two cases?
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$\text{Q}=\frac{\text{V}^2}{\text{R}}\text{t}\propto\frac{1}{\text{R}}$
For same voltage,
$\frac{\text{Q series}}{\text{Q parallel}}=\frac{\text{R parallel}}{\text{R series}}=\frac{\frac{(\text{R.R})}{\text{(R}+\text{R})}}{\text{R}+\text{R}}=\frac{\frac{\text{R}}{2}}{2\text{R}}=\frac14$
For same voltage,
$\frac{\text{Q series}}{\text{Q parallel}}=\frac{\text{R parallel}}{\text{R series}}=\frac{\frac{(\text{R.R})}{\text{(R}+\text{R})}}{\text{R}+\text{R}}=\frac{\frac{\text{R}}{2}}{2\text{R}}=\frac14$
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