A circuit consists of five identical conductors as shown in the figure. The two similar conductors are added as indicated by the dotted lines. The ratio of resistances before and after addition will be :
Answer & explanation
Correct answer: option 3
Before addition,
Total resistance of the circuit is R1 = 5Ω
After addition the two conductors, the circuit will acquire the form as shown in figure
It is a balanced Wheatstone bridge. Resistance of central conductor is ineffective.
∴ Total resistance of the circuit is
$R_2=1 Ω+\frac{(2 Ω)(2 Ω)}{(2 Ω+2 Ω)}+1 Ω=1 Ω+1 Ω+1 Ω=3 Ω$
∴ $\frac{R_1}{R_2}=\frac{5}{3}$