Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is
AIIMS 2000, Medium
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(d) Power consumed means heat produced.
For constant potential difference ${P_{{\rm{consumed}}}} = {\rm{Heat}} \propto \frac{1}{{{R_{eq}}}}$
$\therefore \frac{{{H_1}}}{{{H_2}}} = \frac{{{R_2}}}{{{R_1}}} = \frac{{R/2}}{{2R}} = \frac{1}{4}$
(Since ${R_2} = \frac{{R.R}}{{R + R}} = \frac{R}{2}$and ${R_1} = R + R = 2R)$
For constant potential difference ${P_{{\rm{consumed}}}} = {\rm{Heat}} \propto \frac{1}{{{R_{eq}}}}$
$\therefore \frac{{{H_1}}}{{{H_2}}} = \frac{{{R_2}}}{{{R_1}}} = \frac{{R/2}}{{2R}} = \frac{1}{4}$
(Since ${R_2} = \frac{{R.R}}{{R + R}} = \frac{R}{2}$and ${R_1} = R + R = 2R)$
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