Question

In a long uniform coil of inductance 2l and associated resistance 2r ohms is physically cut in to two exact halves which are rewound in parallel. the resistance and inductance of the combination are

Answer 1

A long uniform coil of inductance 2L and associated resistance 2r Ω.
we know, R is directly proportional to length when corss section of wire keeping constant.{ ∵ R = ρL/A }
so, if coil of resistance 2r , cut halved ,resistance of each part is r.

Now, inductance , L is directly proportional to N² { number of turns } and inversely proportional to length of coil .
so, if coil of inductance 2L , cut halved , inductance of each part is L

Now, both the part are in parallel ,
so, resistance will be
1/Req = 1/R₁ + 1/R₂ = 1/r = 1/r = 2/r
Req = r/2

Inductance will be
1/Leq = 1/L₁ + 1/L₂ = 1/L + 1/L
1/Leq = 2/L ⇒Leq = L/2