The ratio of heat produced in series and parallel combination of two conducting wires can be determined by applying the concept of electrical resistance and power dissipation.
When the wires are connected in series, the total resistance of the combination is given by the sum of the individual resistances of the wires. Since the wires are of the same material, length, and diameter, their resistances will be equal. Therefore, the total resistance in the series combination is twice the resistance of a single wire.
When the wires are connected in parallel, the total resistance of the combination is given by the reciprocal of the sum of the reciprocals of the individual resistances. Again, since the wires are identical, their resistances are equal. Thus, the total resistance in the parallel combination is half the resistance of a single wire.
Now, let's consider the power dissipated in each combination. The power dissipated in a resistor is given by the formula: P = (V^2)/R, where P is the power, V is the potential difference, and R is the resistance.
For the series combination, the power dissipated is proportional to the resistance (since V is the same for both combinations). Therefore, the power dissipated in the series combination is twice the power dissipated in a single wire.
For the parallel combination, the power dissipated is inversely proportional to the resistance. Thus, the power dissipated in the parallel combination is half the power dissipated in a single wire.
Based on the above analysis, the ratio of heat produced in series and parallel combination is 2:1. Therefore, the correct answer is B. 2:1.
