Question

You have three identical resistors that you can connect in various ways. Which of the following is NOT a possible value of the equivalent resistance of the three-resistor combinations?A. 3RB. R/3 C. 2R/3D. 3R/2

Answer 1

Answer: option c.

Explanation: 3 identical resistors can only have 3 configurations

1) all 3 resistors in series

2) all 3 resistors in parallel

3) 2 parallel resistors in series with 1 resistor.

Case 1 : all 3 resistors in series

Let us assume each of the resistor has resistance value R.

The total resistor (Rt) of 3 resistors in series is given as

Rt = R1 + R2 + R3

Since R1=R2=R3=R

Rt = R+R+R = 3R.

Case 2: all 3 resistors in parallel.

The equivalent resistance of resistors in parallel is given by the formulae below.

1/Rt = 1/R1 + 1/R2 + 1/R3

Since R1=R2=R3=R

1/Rt = 1/R + 1/R + 1/R

1/Rt = 1 +1 +1/ R

1/Rt = 3/R

3 * Rt = R

Rt = R/3

Case 3: 2 parallel resistor in series with one

First is to get the equivalent resistance of the 2 parallel resistor.

1/Rt = 1/R1 + 1/R2

But R1=R2=R

1/Rt = 1/R + 1/R

1/Rt = 1 + 1/R

1/Rt = 2/R

2 *Rt = R

Rt =R/2.

R/2 in series with R has an equivalent resistance as shown below

Rt = R/2 + R

Rt = R + 2R/2

Rt = 3R/2

Since all the possible 3 configuration are listed above and there is no other then option c ( 2R/3) is not possible to achieve