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Four resistances 10 Ω , 5 Ω , 7 Ω and 3 Ω are connected so that they form the sides of a rectangle AB, BC, CD and DA respectively. Another resistance of 10 Ω is connected across the diagonal AC. The equivalent resistance between a A and B is
  • a)
    2 Ω
  • b)
    5 Ω
  • c)
    7 Ω
  • d)
    10 Ω
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Four resistances 10 , 5 , 7 and 3 are connected so that they form ...
Solution:
Given resistances are 10 Ω, 5 Ω, 7 Ω and 3 Ω respectively.

These resistances are connected in the form of a rectangle ABCD.

Resistance of AB = 10 Ω

Resistance of AD = 3 Ω

Resistance of BC = 5 Ω

Resistance of CD = 7 Ω

Resistance of diagonal AC = 10 Ω

To find out the equivalent resistance between A and B.

Let us consider the equivalent resistance between A and D, which is given by

R_AD = 3 + 7 = 10 Ω

Similarly, the equivalent resistance between B and C is given by

R_BC = 5 + 10 = 15 Ω

Now, the equivalent resistance between A and C can be found by applying the parallel combination of R_AD and R_BC.

The equivalent resistance between A and C is given by

1/R_AC = 1/R_AD + 1/R_BC

=> 1/R_AC = 1/10 + 1/15

=> 1/R_AC = 1/6

=> R_AC = 6 Ω

Now, the equivalent resistance between A and B can be found by applying the series combination of AB and AC.

The equivalent resistance between A and B is given by

R_AB = 6 + 10 = 16 Ω

Therefore, the correct option is (B) 5.
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Four resistances 10 , 5 , 7 and 3 are connected so that they form the sides of a rectangle AB, BC, CD and DA respectively. Another resistance of 10 is connected across the diagonal AC. The equivalent resistance between a A and B isa)2 b)5 c)7 d)10 Correct answer is option 'B'. Can you explain this answer?
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