Question

the effective resistance in between the points A and B in the circuit given below
(1)23 ohm
(2)32ohm
(3)12ohm
(4)45ohm​

Answer 1

Answer:

32. ............................

Answer 2

We need to find:

• Effective resistance in between the points A and B of the circuit given.

Knowledge required:

• When two or more resistors are connected in series then the equivalent resistance is given by the sum of all individual resistances.

• When two or more resistors are connected in parallel then the reciprocal of equivalent resistance is given by the sum of reciprocals of all individual resistances.

Solution:

In the figure:

Let us consider left side first

Here, resistances 10Ω and 8Ω are in series and then in parallel to 9Ω.

so, Equivalent resistance of 10Ω and 8Ω will be,

→ R_1 = 10 Ω + 8 Ω = 18 Ω

And, since 9Ω is in parallel to the effective resistance of 10Ω and 8Ω .,so

→ 1/R_2 = 1/18 + 1/9

→ 1/R_2 = ( 1 + 2 ) / 18

→ 1/R_2 = 3/18

→ R_2 = 6 Ω

Now, 14Ω will be in series to the effective resistance of 9Ω, 10Ω and 8 Ω.,

therefore,

→ R_3 = 14 Ω + 6 Ω = 20 Ω

We have calculated the effective resistance of the left-hand side circuit.

Now, Let's consider the right side

Here, in the figure

5 Ω and 15 Ω are in series and, then in parallel to 20Ω, so

The Equivalent resistance of 5 Ω and 15 Ω will be,

→ R_4 = 5 Ω + 15 Ω = 20 Ω

and, 20Ω is in parallel to the effective resistance of 5 Ω and 15Ω., so

→ 1/R_5 = 1/20 + 1/20

→ 1/R_5 = 2/20

→ R_5 = 10 Ω

Further,

6 Ω resistor would be in series to the equivalent resistance of 5 Ω, 15Ω and 6Ω., therefore,

→ R_6 = 6 Ω + 10 Ω = 16 Ω

Now, this resistance R_6 will be in parallel to 48 Ω resistor

Hence, combined resistance will be,

→ 1/R_7 = 1/48  +  1/16

→ 1/R_7 = ( 1 + 3 ) / 48

→ R_7 = 12 Ω

Here, we have cleared all resistances of the right side.,

and we have the equivalent resistance of left side circuit as '20 Ω', that is in series to the equivalent resistance of right side circuit as '12 Ω'.

Hence,

Equivalent resistance between the points A and B will be,

→ R(eq) = 12 Ω + 20 Ω = 32 Ω.

therefore,

• OPTION (2) 32 ohm is the correct Answer.