Question

QQ.4 resistors each of resistance 2ohm are joined end to end form a square ABCD. Calculate the equivalent resistance of the combination between any two adjacent corners ?

Answer 1

Step-by-step explanation:

Solution:

The given configuration is shown in attached figure.

To Calculate the equivalent resistance of the combination between any two adjacent corners ,let us take AB adjacent corners

So,resistors between other three sides are in series

$\begin{gathered}R_{s} = R_{bc} + R_{cd} + R_{ab} \\ \\ R_{s} = 2 + 2 + 2 \\ \\ = 6 \: ohm \\ \end{gathered}$

Now, 6 ohm is parallel with resistance of 2 ohm

$\begin{gathered} \frac{1}{R_{eq}} = \frac{1}{R_{s}} + \frac{1}{R_{ab}} \\ \\ = \frac{1}{6} + \frac{1}{2} \\ \\ = \frac{1 + 3 }{6} \\ \\ = \frac{4}{6} \\ \\ = \frac{2}{3} \\ \\ R_{eq} = \frac{3}{2} \\ \\ R_{eq} = 1.5 \: ohm \\ \\ \end{gathered}$