Question

Rewrite the equation to represent the resistance of resistor 2, R2, in terms of RT and R1.

A. R2 = RTR1/R1-1
B. R2 = R1 + R2/RT R1
C. R2 = RT - R1/RTR1
D. R2 = RT R1/R1-RT

Answer 1

The equation that represents the resistance of resistor 2, R2, in terms of RT and R1 is D. R2 = RT R1/(R1-RT).

Step-by-step explanation:

To understand why this equation is correct, let's break it down:

In the given information, we know the equivalent resistance of Rs1 and Rs2 (in parallel) is Rp2 = 1/(1/RS1 + 1/RS2) = 29.09 Ω.

Next, we replace the upper resistors R2 and R3 with the equivalent resistor R$1, and the lower resistors Rp1 and R6 with the equivalent resistor Rs2.

So, the total resistance is Rtot = R$1 + Rp1 + R6.

Using the formula for resistors in parallel, we find that R$1 = R2*R3/(R2 + R3). Similarly, Rp1 = 1/(1/Rs1 + 1/Rs2).

Finally, we combine resistors R1 and Rp2 (in series) to get the total resistance Rtot = R1 + Rp2.

Combining these steps, we can rewrite the equation as R2 = RT R1/(R1-RT).

Therefore the correct answer is D. R2 = RT R1/(R1-RT).