Question

find the equivalent resistance across the two ends A and B of the circuit shown.

Don't spam ✖​

Answer 1

Answer:

Clearly R1 and R2 are in parallel.

The equivalent resistance R12 of R1 and R2 will be given by,

★1/ R12 = 1/R1 + 1/R2

➡1/2+1/2 ( Using Given values of resistance)

or 1/R12 = 1/1

or 1/R12 = 1 ohm

Similarly ,

equivalent resistances , R34 ( of R3 and R4) , R56( of R5 and R6) and R78( of R7 and R8) will also be 1 ohm.

Now,

R12 and R34 are in series.

Their equivalent resistance , R1234 = R12 +R34

==> 1ohm + 1ohm = 2ohm

Also,

R78 and R56 are in series.

Their equivalent resistance, R5678 = R56 +R78

==> 1ohm +1ohm = 2ohm

So , The Given circuit can now be represented as shown.

Now,

R1234 and R5678 are in parallel

Their equivalent resistance, Re will be Given by,

1/Re= 1/R1234 + 1/ R5678

➡ 1/2 + 1/2 =1/1

➡ Re = 1 ohm

Thus, the equivalent resistance between A and B is 1 ohm.

___________________________

Answer 2

Answer:

SOLUTION:-

Clearly R1 and R2 are in parallel.

The equivalent resistance R12 of R1 and R2 will be given by,

★1/ R12 = 1/R1 + 1/R2

➡1/2+1/2 ( Using Given values of resistance)

or 1/R12 = 1/1

or 1/R12 = 1 ohm

Similarly ,

equivalent resistances , R34 ( of R3 and R4) , R56( of R5 and R6) and R78( of R7 and R8) will also be 1 ohm.

Now,

R12 and R34 are in series.

Their equivalent resistance , R1234 = R12 +R34

==> 1ohm + 1ohm = 2ohm

Also,

R78 and R56 are in series.

Their equivalent resistance, R5678 = R56 +R78

==> 1ohm +1ohm = 2ohm

So , The Given circuit can now be represented as shown.

Now,

R1234 and R5678 are in parallel

Their equivalent resistance, Re will be Given by,

1/Re= 1/R1234 + 1/ R5678

➡ 1/2 + 1/2 =1/1

➡ Re = 1 ohm

Thus, the equivalent resistance between A and B is 1 ohm.

___________________________