Question

13. Find equivalent resistance across A and B
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Answer 1

Answer:

IF ALL ARE ARRANGED INTO PARALLEL RESISTORS

THEN,THE EQUIVALENT RESISTANCE WILL BE

$\frac{1}{R} \times 6 = equivalent \: resistence \\ = \frac{6}{R} \\HOPE \:IT \:HELPS \:U\::)$

Answer 2

Solution :

Please refer the attachment first !!!

Step I : connect a battery across the circuit

Step II : write potential across resistors

[ The potential across both the ends of the wire will be the same .

Consider the unknown point as x

Step III : Rearrange the circuit

Point X and B

Three resistors are connected in parallel to each other .

Equivalent resistances for n no of resistors is connected in parallel is given by ,

➜   1 / Rp = 1 / R 1 + 1 / R 2 .... + 1 / Rn

Hence ,

➜  1 / Rp = 1 / R  + 1 / R + 1 / R

➜  1 / Rp = 3 / R

➜  Rp = R / 3 Ω

Point A and B

R and R/3 are connected in series with each other .

Equivalent resistances for n no of resistors is connected in series is given by ,

➜   Rs = R 1 + R 2 .... + Rn

Hence ,

➜  Rs = R + R / 3

➜  Rs = 4R / 3Ω

Now ,

R , 3R/2 , R are connected in parallel with each other .

➜  1 / Rp = 1 / R + 3 / 4R + 1 / R

➜   1 / Rp = 2 / R + 3 / 4R

➜  1 / Rp = 8+ 3 / 4R

➜  1 / Rp = 11 / 4R

➜  Rp = 4R / 11 Ω

The net equivalent resistance of the circuit is 4R/11 Ω