Question

Equivalent resistance between points A and B is
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Answer 1

SoLuTioN :

⏭ Given:

✏ A diagram of six resistors.

⏭ To Find:

✏ Equivalent resiatance between A and B

✏ Please see the attachment for better understanding...

⏭ Calculation:

✏ For wheat-stone bridge condition...

$\mapsto \sf \: \frac{1}{R_{eq}} = \frac{1}{2R} + \frac{1}{2R} + \frac{1}{R} \\ \\ \mapsto \sf \: \frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} \\ \\ \mapsto \sf \: \frac{1}{R_{eq}} = \frac{2}{R} \\ \\ \star \: \underline{ \boxed{ \bold{ \sf{ \orange{R_{eq} = \frac{R}{2} \: \Omega}}}}} \: \star$

Answer 2

Answer:

Given:

A circuit has been provided.

To find:

Equivalent resistance of the circuit

Concept:

In this kind of complex circuits , you need to first form a simplified circuit. Then find out the equivalent resistance by assigning Parallel or Series combination.

The best way to form the simplified circuit is by assigning potential drops along the resistances.

Diagram:

The simplified circuit has been provided in the attachment , please refer to it for better understanding.

Calculation:

We can very well see that the upper part of the circuit has a balanced Wheatstone Bridge configuration.

As a result the middle resistance won't be considered.

So we see that 2R , 2R and R resistances are in parallel.

$\dfrac{1}{R \: eq.} = \dfrac{1}{2R} + \dfrac{1}{2R} + \dfrac{1}{R}$

$= > \dfrac{1}{R \: eq.} = \dfrac{2}{ R }$

$= > R \: eq. = \dfrac{R}{2}$