Question

Two resistors connected in series have an equivalent resistance of 734 omega. When they are connected in parallel, their equivalent resistance is 124 omega. Calculate the resistance of each resistor. Enter the smaller one first.

Answer 1

To calculate the resistance of each resistor given the series and parallel equivalent resistances, one must solve two equations symbolizing the sum of resistances in series and the inverse of the sum of the reciprocals in parallel.

Step-by-step explanation:

To find the resistance of each resistor when two resistors are connected in series and their equivalent resistance is 734 Ω (ohms), and in parallel, their equivalent resistance is 124 Ω, we need to use the formulas for resistors in series and parallel.

For resistors in series, the equivalent resistance (Req-ser) is the sum of the individual resistances:

R1 + R2 = 734 Ω

For resistors in parallel, the equivalent resistance (Req-par) is given by:

1 / Req-par = 1 / R1 + 1 / R2

1 / 124 Ω = 1 / R1 + 1 / R2

We have a system of equations:

R1 + R2 = 734 Ω1 / R1 + 1 / R2 = 1 / 124 Ω

After solving this system, we find that R1 and R2 are the resistances of the two resistors. Let's say R1 is the smaller one. The resistances can be found by solving for both variables using algebraic techniques such as substitution or elimination.