Two conducting wires of the same material

solution:

Since both the wires are made of the same material and have equal lengths and equal diameters,

they have the same resistance. Let it be R.

When connected in series, their equivalent resistance is given by

$\mathrm{R}_{\mathrm{s}}=\mathrm{R}+\mathrm{R}=2 \mathrm{R}$

When connected in parallel, their equivalent resistance is given by

$\frac{1}{R_{p}}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}$ or $R_{p}=\frac{R}{2}$

Further, electrical power is given by $P=\frac{V^{2}}{R}$

Power (or heat produced) in series, $P_{s}=\frac{V^{2}}{R_{s}}$

Power (or heat produced) in parallel, $P_{p}=\frac{V^{2}}{R_{p}}$

Thus, $\frac{P_{s}}{P_{p}}=\frac{V^{2} / R_{s}}{V^{2} / R_{p}}=\frac{R_{p}}{R_{s}}=\frac{R / 2}{2 R}=\frac{1}{4}$

or $P_{s}: P_{p}=1: 4$

Thus, (3) is the correct answer.