Problem Statement:
Two coils, each with a resistance of 250 ohms, are connected in series across a constant voltage. We need to calculate the value of the resistance that should be connected in parallel with one of the coils to reduce the potential difference across its terminals by 1%.

Solution:

Step 1: Understanding the Problem
We have two coils connected in series across a constant voltage. When the voltage is applied, the potential difference across each coil will be determined by the resistance of the coil. We need to reduce the potential difference across one of the coils by 1% by connecting a resistance in parallel with it.

Step 2: Calculation of Potential Difference
The potential difference across a coil in a series circuit can be calculated using Ohm's law:
V = IR

Where:
V is the potential difference across the coil
I is the current flowing through the circuit
R is the resistance of the coil

In our case, the resistance of each coil is given as 250 ohms. Since the coils are connected in series, the total resistance of the circuit will be the sum of the individual resistances:
R_total = R1 + R2
= 250 + 250
= 500 ohms

The current flowing through the circuit will be the same for both coils since they are in series. Let's assume the current is I.

The potential difference across each coil can be calculated as:
V1 = IR1
V2 = IR2

Step 3: Calculation of New Potential Difference
To reduce the potential difference across one of the coils by 1%, we need to calculate the new potential difference and then find the resistance that should be connected in parallel.

Let's assume the potential difference across the first coil is V1'. Since we want to reduce it by 1%, the new potential difference will be:
V1' = V1 - (0.01 * V1)

Step 4: Calculation of New Resistance
To calculate the resistance that should be connected in parallel with the first coil, we can use the formula for resistors in parallel:
1/R_total' = 1/R1 + 1/R_parallel

Where:
R_total' is the new total resistance
R1 is the resistance of the first coil (250 ohms)
R_parallel is the resistance we need to find

Substituting the values:
1/R_total' = 1/250 + 1/R_parallel

We can rearrange the equation to solve for R_parallel:
1/R_parallel = 1/R_total' - 1/R1

Finally, we can find the value of R_parallel by taking the reciprocal of both sides:
R_parallel = 1 / (1/R_total' - 1/R1)

Substituting the values:
R_parallel = 1 / (1/500 - 1/250)

Step 5: Calculation
Now, let's calculate the value of R_parallel:
R_parallel = 1 / (1/500 - 1/250)
= 1 / (2/500 - 1/250)
= 1 / (2/500 - 2/500)
= 1 / 0
= Undefined

Conclusion:
The value of resistance that should be connected in parallel