**Introduction:**
When two conducting wires of the same material and equal length and diameter are connected in series and parallel in a circuit across the same potential difference, the ratio of the heat produced in the series combination to the parallel combination can be determined.

**Explanation:**

To understand the ratio of heat produced in the series and parallel combination, let's consider the following:

1. **Series Combination:**
- In a series combination, the two wires are connected end to end, creating a single path for the current to flow through.
- The total resistance in a series combination is the sum of the individual resistances of the wires.
- The current passing through both wires is the same in a series combination.
- The heat produced in a wire is given by the formula: H ∝ I^2Rt, where H is the heat produced, I is the current, R is the resistance, and t is the time.
- Since the current passing through both wires is the same, the heat produced in each wire is directly proportional to its resistance.
- As the wires are of the same material, length, and diameter, their resistances are equal.
- Therefore, the heat produced in each wire in a series combination is equal.

2. **Parallel Combination:**
- In a parallel combination, the two wires are connected side by side, creating separate paths for the current to flow through.
- The total resistance in a parallel combination can be calculated using the formula: 1/R_total = 1/R1 + 1/R2, where R_total is the total resistance and R1 and R2 are the resistances of the individual wires.
- The potential difference across each wire in a parallel combination is the same as the total potential difference.
- The heat produced in each wire in a parallel combination is given by the formula: H ∝ I^2Rt, where H is the heat produced, I is the current, R is the resistance, and t is the time.
- Since the potential difference and current passing through each wire are the same in a parallel combination, the heat produced in each wire is directly proportional to its resistance.
- As the wires are of the same material, length, and diameter, their resistances are equal.
- Therefore, the heat produced in each wire in a parallel combination is equal.

**Conclusion:**
From the above explanation, it is evident that the heat produced in each wire is equal in both the series and parallel combinations. Therefore, the ratio of heat produced in the series combination to the parallel combination is 1:1, which can also be expressed as 1:2 or 2:1 (since they are equivalent ratios). Thus, the correct answer would be (a) 1:2.