Question

a uniform wire of resistance 20 ohm is bent into a circular form. what will be the effective resistance across the ends of its one diameter?

Answer 1

as we know,
$\bold{R=\rho\frac{L}{A}}$
here, R is resistance , ρ is resistivity , L is length of wire and A is corss section area of wire .
It means when length of wire is halved without changing the cross section area , resistance will be half.
so, both half circular part has R/2 = 10 Ω resistance
now, A/C to question,
we have to find the resistance across the ends of its diameter .
means both the semi circular resistors of place like parallel combination .
so, equivalent resistance across the ends of its diameter is :
1/Req = 1/R₁ + 1/R₂
1/Req = 1/10Ω + 1/10Ω = 2/10Ω = 1/5Ω
Req = 5Ω

Hence, answer is 5Ω