A 100-Rresistor and another resistor in parallel have an equivalent resistance of 75 R. What is the resistanceof the other resistor?

Sure, let's solve this step by step.

Step 1: Understand the problem We have two resistors in parallel. One is 100 ohms and the other we don't know. The total resistance of the circuit is 75 ohms. We need to find the resistance of the unknown resistor.

Step 2: Use the formula for resistors in parallel The formula for total resistance (Rt) for two resistors in parallel is given by:

1/Rt = 1/R1 + 1/R2

where R1 and R2 are the resistances of the two resistors. In this case, Rt is 75 ohms and R1 is 100 ohms.

Step 3: Substitute the known values into the formula Substituting the known values into the formula gives us:

1/75 = 1/100 + 1/R2

Step 4: Solve for R2 To solve for R2, we first subtract 1/100 from both sides of the equation:

1/75 - 1/100 = 1/R2

Then, we take the reciprocal of both sides to solve for R2:

R2 = 1 / (1/75 - 1/100)

Step 5: Calculate the value When you calculate the value, you find that R2 is approximately 300 ohms. So, the resistance of the other resistor is 300 ohms.