Question

Find the effective resistance between A and B.​

Answer 1

In the above figure, we have to find the effective resistance between A and B .

I have named the joints for convinience while solving the question ...

On carefully observing the figure , you can observe symmetry in the figure ..

So , one method to solve this question is by using symmetry .

However , I am solving by an easier method ..

Here , on observing carefully , you can find that no current flows through the resistor FGE to AB

Similarly no current flows through the resistor CGD into AB .

So , the above figure can be redrawn as -

Refer to the second attached image .

Now , after this change is made, solving the question becomes easier ...

We know that -

When n number of resistors are in series, effective resistance = r1 + r2 + ......... + rn

When n numbers of resistors are connected in parallel ,

1 / Equivalent Resistance = 1 / R1 + 1 / R2 + ....... + 1 / R n

Now , in the figure , let us observe the resistors FE and FG'E .

They are connected in series and parallel .

So ,

1 / Equivalent Resistance FE

=> ( 1 / 2 R ) + ( 1 / R )

=> Equivalent Resistance FE

=> ( 2 / 3 ) R

Similarly ,

Equivalent Resistance CD = ( 2 / 3 ) R .

So , the figure simplifies further -

See the third attached image for reference.

Now ,

Resistance AFEB

=> R + ( 2 / 3 ) R + R

=> ( 8 / 3 ) R

Similarly resistance ACDB = ( 8 / 3 ) R

See the fourth attached image for the diagram ...

Here , the three resistors are in parallel .

Equivalent Resistance -

( 1 / R eq )

=> ( 3 / 8 R ) + ( 1 / 2R ) + ( 3 / 8 R )

=> ( 5 / 4 R )

=> R equivalent = ( 4 / 5 ) R

Hence , the required effective resistance in this circuit is ( 4 / 5 ) R .

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