Question

Five identical resistance coils are connected in the network as shown in fig and the resistance measured between A and B is 1 ohm.Then the individual coils must have a resistance of:-
A) 1 ohm
B) 1/4 ohm
C)7/4 ohm
D)4/7 ohm

Answer 1

Answer: 7/4

Explanation:

Refer to attached file for explanation

Answer 2

Given : Five identical resistance coils are connected in the network as shown in fig and the resistance measured between A and B is 1 Ω.

To find : the resistance of each resistor.

solution : Let R is the resistance of each resistor.

Three resistors are joined in parallel combination.

let R₁ is the equivalent resistance of three resistors.

so, 1/R₁ = 1/R + 1/R + 1/R

⇒R₁ = R/3

now R₁ and R are joined in series combination.

so equivalent resistance, R₂ = R₁ + R = R + R/3

= 4R/3

finally, R₂ and R are joined in parallel combination.

1/Req = 1/R₂ + 1/R

= 1/(4R/3) + 1/R

= 3/4R + 4/4R

= 7/4R

⇒Req = 4R/7 = 1 Ω

⇒R = 7/4 Ω

Therefore the individual coils must have a resistance of 7/4 Ω.