Question

Three resistances are connected to form the sides of a triangle ABC. The resistance of sides AB, BC and CA are 40ohm 60 ohm and 100 ohm respectively.

Calculate the effective resistance Calculate the effective resistance across AC.

Answer 1

Three resistances are connected to form the sides of a triangle ABC. The resistance of sides AB, BC and CA are 40ohm 60 ohm and 100 ohm respectively.

Assume a triangle ABC having AB 40 ohm, BC 60 ohm and CA 100 ohm.

We have to find the effective resistance across AC.

Looking at attachment we can say that, both AB and BC are connected in series.

------| R1 = 40 ohm |--------| R2 = 60 ohm |-----

Rs = R1 + R2

Rs = (40 + 60) ohm

Rs = 100 ohm

Now, the resultant of series and R3 are connected in parallel. So, for parallel combination:

--------------| Rs = 100 ohm |-------------

--------------| R3 = 100 ohm |-------------

1/Rp = 1/Rs + 1/R3

1/Rp = 1/100 + 1/100

1/Rp = 2/100

1/Rp = 1/50

Rp = 50 ohm

Req = Rp = 50 ohm

Answer 2

Answer:

YOUR QUESTION :

Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will be [JIPMER 2002]

YOUR ANSWER : 32 ohm.

ANSWER EXPLANATION :

Firstly,

according to the question's given condition

40ohm and 60 ohm are series so,

$R = R(ac) + R (cb) \\ R = 100 + 60 \\R = 160 ohm ----------( 1 ) </p><p></p><p></p><p></p><p></p><p>$

This R is parallel to 40 ohm,

therefore,

1 / R = 1 / 40 + 1 / 160

1 / R = 5 / 160

R = 160/5

R = 32 ohm.