Question

15. The equivalent resistance between A and B is :
(1)3/4r
(2)5/3r
(3)7/5r
(4)r​

Answer 1

Given :

▪ A circuit having six identical resistor of resistance R has been provided.

To Find :

✴ Eq. resistance b/w A and B.

Concept :

❇ In this type of questions, First we have to simplify the given circuit.

❇ We can simplify any circuit by potential method.

Diagram :

↗ Please see the attachment for better understanding.

Calculation :

⚽ Eq. resistance b/w C and D :

→ R1 = R/2 + R

→ R1 = 3R/2Ω

⚽ Eq. resistance b/w E and F :

→ R2 = R + R/2

→ R2 = 3R/2Ω

⚽ Eq. resistance b/w A and B :

→ 1/Req = 1/R1 + 1/R2

→ 1/Req = 2/3R + 2/3R

→ Req = (3R/2) / 2

→ Req = 3R/4Ω

Answer 2

In the above Question , we have to find the equivalent Resistance between A and B .

To make the question easier to solve , I have named all the points .

Solution -

Observe the above figure carefully .

Here ,

The resistances PD and PBD are parallel to each other .

We know that -

For resistances In a parallel connection of n resistors ,

( 1 / Equivalent Resistance )

=> ( 1 / r 1 ) + ( 1 / r 2 ) + ........ + ( 1 / R n )

So ,

Effective resistance Of PD

=> [ R × R ] / 2 R

=> R / 2 Ohm

Similarly we can calculate the effective resistance of QC to be

( R / 2 ) Ohm

Now ,

The figure can also be drawn as ...

See the second attached image .

Here , MQ is in series with QP

We know that -

For a connection of n resistors in series ,

Equivalent Resistance

=> R 1 + R 2 + ........ + R n

So ,

Equivalent Resistance MP

=> R + R/2

=> ( 3 R / 2 ) Ohm

Similarly the equivalent Resistance CN

is also ( 3 R / 2 ) Ohm

Now the new figure becomes -

See the third attached image .

Now , the resistances are in parallel .

We know that -

For resistances In a parallel connection of n resistors ,

( 1 / Equivalent Resistance )

=> ( 1 / r 1 ) + ( 1 / r 2 ) + ........ + ( 1 / R n )

So ,.

1 / {Effective Resistance AB }

=> ( 2 / 3R ) × 2

=> ( 4 / 3 R )

=> Effective Resistance AB = 3R / 4 .

Hence , Option 1 is the correct answer .