Analyzing the Circuit:
To understand the relationship between the equivalent resistances of R1 and R2 in series and parallel, let's first analyze the basic circuit configurations.

Series Connection:
When resistors are connected in series, the current flowing through each resistor is the same. In this configuration, the total resistance (R_total) is equal to the sum of the individual resistances (R1 + R2), according to Ohm's Law.

Parallel Connection:
When resistors are connected in parallel, the voltage across each resistor is the same. In this configuration, the reciprocal of the total resistance (1/R_total) is equal to the sum of the reciprocals of the individual resistances (1/R1 + 1/R2), according to the rules of parallel resistances.

Determining the Equivalent Resistances:
Let's assume that the equivalent resistance of R1 in series is r1, and the equivalent resistance of R2 in parallel is r2. We can express this relationship mathematically as:

R_total = r1
1/R_total = 1/r2

Solving the Equations:
To find the relationship between R1 and R2, we can substitute the series and parallel resistance equations:

R_total = r1 = R1 + R2
1/R_total = 1/r2 = 1/(1/R1 + 1/R2)

Simplifying the Equations:
To simplify the equation, we can take the reciprocal of both sides:

1/R_total = 1/r2
R_total = r2

Since R_total = r1, we can substitute r1 = r2:

r1 = r2

Conclusion:
From the above analysis, we can conclude that when the equivalent resistance of R1 in series is r1 and the equivalent resistance of R2 in parallel is r2, the ratio R1/R2 is always equal to 1. This implies that R1 and R2 have the same value.

In summary, the ratio R1/R2 is always equal to 1 for resistors connected in such a way that the equivalent resistance of R1 is r1 and the equivalent resistance of R2 is r2. It signifies that R1 and R2 have the same resistance value.

Yes