Explanation:
Assuming resistance of heater wire \({=R}\)
Case I: When two heater wires are connected in series,
Heat produced \( = {H_s} = {V^2}t/2R\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
Case II: When two heater wires are connected in parallel,
Net resistance \({=R / 2}\)
\({H_p} = \frac{{{V^2}t}}{{R/2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
Dividing eqns. (1) and (2)
\({\dfrac{H_{s}}{H_{p}}=\dfrac{V^{2} t}{2 R} \times \dfrac{R / 2}{V^{2} t} \Rightarrow \dfrac{H_{s}}{H_{p}}=\dfrac{1}{4}}\).
So correct option is (2)