SATHEE: Current Electricity - Result Question 37

Current Electricity - Result Question 37

39. In the network shown in the Fig, each resistance is $1 Ω$ . The effective resistance between $A$ and $B$ is

(a) $\frac{4}{3} Ω$

(b) $\frac{3}{2} Ω$

(d) $\frac{8}{7} Ω$

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Answer:

Correct Answer: 39. (d)

Solution:

(d) At $A$ current is distributed and at $B$ currents are collected. Between $A$ and $B$ , the distribution is symmetrical. It has been shown in the figure. It appears that current in $A O$ and $O B$ remains same. At $O$ , current $i_{4}$ returns back without any change. If we detach $O$ from $A B$ there will not be any change in distribution.

Now, $Misplaced &$ will be in series hence its total resistance $= 2 Ω$

It is in parallel with $C D$ , so, equivalent resistance

$= \frac{2 \times 1}{2 + 1} = \frac{2}{3} Ω$

This equivalent resistance is in series with $A C$ $Misplaced &$ , so, total resistance

$= \frac{2}{3} + 1 + 1 = \frac{8}{3} Ω$

Now $\frac{8}{3} Ω$ is parallel to $A B$ , that is, $2 Ω$ , so total resistance

$= \frac{8 / 3 \times 2}{8 / 3 + 2} = \frac{16 / 3}{14 / 3} = \frac{16}{14} = \frac{8}{7} Ω$

Between $Misplaced &$ , the equivalent resistance is given by

$1 / r = \frac{1}{r_{3}} + \frac{1}{(r_{4} + r_{5})} = 1 + \frac{1}{2} = \frac{3}{2}$

Equivalent resistance along

$A C D B = 1 + \frac{2}{3} + 1 = \frac{8}{3}$

$∴$ Effective resistance between $A$ and $B$ is

$. \frac{1}{R} = \frac{3}{8} + \frac{1}{2} = \frac{7}{8} or R = \frac{8}{7} Ω]$

Current Electricity - Result Question 37

39. In the network shown in the Fig, each resistance is $1 Ω$ . The effective resistance between $A$ and $B$ is

Answer:

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Current Electricity - Result Question 37

39. In the network shown in the Fig, each resistance is 1Ω. The effective resistance between A and B is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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39. In the network shown in the Fig, each resistance is $1 Ω$ . The effective resistance between $A$ and $B$ is