Three parallel resistors have a total conductance of 2 mS. If two of the resistances are 1 and 5 kR,what isthe third resistance?

Sure, here are the steps to solve the problem:

Step 1: Convert the total conductance to total resistance. The formula to convert conductance (G) to resistance (R) is R = 1/G. So, the total resistance (Rt) is 1/2 mS = 500 ohms.

Step 2: The total resistance of parallel resistors is given by the formula 1/Rt = 1/R1 + 1/R2 + 1/R3. We know Rt, R1 and R2, so we can solve for R3.

Step 3: Substitute the known values into the formula: 1/500 = 1/1000 + 1/5000 + 1/R3.

Step 4: Simplify the equation: 0.002 = 0.001 + 0.0002 + 1/R3.

Step 5: Subtract 0.001 and 0.0002 from both sides of the equation to isolate 1/R3: 0.002 - 0.001 - 0.0002 = 1/R3, which simplifies to 0.0008 = 1/R3.

Step 6: Finally, solve for R3 by taking the reciprocal of both sides: R3 = 1/0.0008 = 1250 ohms or 1.25 kR.

So, the third resistance is 1.25 kR.