Question

Show how would you join three resistor each of resistance 9 ohm so that the equivalent resistance of the combination is 1 13.5 ohm 2 6 ohm

Answer 1

1st
2 resistors in parallel and 1 in series.

2nd
2 in series and 1 in parallel.

Answer 2

The equivalent resistance can be obtained by the combination of resistors connected in series and parallel to form 13.5 ohm and 6 ohm.

Solution:

(a) Image 1: For the equivalent resistance to be 13.5 ohm, the following arrangement of combination of 9 ohm each resistance has to be joined in circuit of three resistance.

The first two resistors would be connected in parallel and third one is connected in series with the first two parallel resistors.

$\begin{array}{l}{R=\frac{1}{R_{1}}+\frac{1}{R_{2}}=\left(\frac{1}{9}+\frac{1}{9}\right)=\frac{2}{9}=\frac{1}{4.5}} \\ {R=4.5 \text { ohm }} \\ {R_{e f f}=R+R_{3}=4.5+9=13.5 \text { ohm }}\end{array}$

(b) Image 2: For equivalent resistance to be 6 ohm, the following arrangement of combination of 9 ohm each resistance has to be joined in circuit of three resistance.

The first two resistors would be connected in series and third one is connected in parallel with the first two series resistors.

$\begin{array}{l}{R=R_{1}+R_{2}=9+9=18} \\ {\frac{1}{R_{e f f}}=\frac{1}{R}+\frac{1}{R_{3}}=\frac{1}{18}+\frac{1}{9}=\frac{3}{18}=\frac{1}{6}} \\ {R_{e f f}=6 \text { ohm }}\end{array}$