Answer to Question #226069 in Electric Circuits for Kunal

Question

A wire of length 2l is and resistance 2R is cut into two pieces and

then stretched twice of its previous length. Now first the:

connected in series the equivalent resistance is R, then they are

connected in parallel the equivalent resistance is Ry. The ratio

 R2,:R1, would be

Answer 1

Initial length (l)=2l

Resistance(R)=2R

Cut in two pieces

R'=R;

R''=R

First series combination

$R_1=R'+R''$

$R_1=R+R=2R$

Parralled combination

$\frac{1}{R_2}=\frac{1}{R'}+\frac{1}{R''}$

$\frac{1}{R_2}=\frac{1}{R}+\frac{1}{R}$

$\frac{1}{R}=\frac{2}{R}$

$R_2=\frac{R}{2}$

$\frac{R_2}{R_1}=\frac{\frac{R}{2}}{2R}=\frac{1}{4}$