Question

Five identical resistance coils are connected in the network as shown in fig. and ht resistance measured between A and B is 1Ω. Then the individual coils must have a resistances of :-

• A. 1Ω
• B. $\frac{1}{4}$ Ω
• C. $\frac{7}{4}$ Ω
• D. $\frac{4}{7}$ Ω

Answer 1

Answer: (A)

1Ω

Answer 2

The circuit consists of five identical resistance coils arranged in a Wheatstone bridge configuration. If all five resistors are identical (resistance R), the bridge is balanced because the ratio of resistances in the arms is equal (R/R = R/R). In a balanced Wheatstone bridge, no current flows through the diagonal resistor, so it can be removed. The circuit simplifies to two parallel branches, each having two resistors in series (R+R = 2R). The equivalent resistance of these two parallel 2R branches is $(2R \times 2R) / (2R + 2R) = 4R^2 / 4R = R$. Given that the total equivalent resistance between A and B is 1Ω, the individual coil resistance R must be 1Ω.