A wire of given material having length l and area of cross section A, has a resistance of 2 ohms. Find the resistance of another wire of same material having length 2l and area of cross section A/2.

Open in App

Solution

$R e s i s \tan c e o f t h e w i r e i s g i v e n b y : R = \frac{ρ l}{A} w h e r e ρ i s t h e r e s i s t i v i t y o f t h e m a t e r i a l w h i c h i s c o n s \tan t f o r t h e p a r t i c u a l r m a t e r i a l . f o r t h e f i r s t w i r e R_{1} = \frac{ρ l}{A} = 2 f o r t h e s e c o n d w i r e R_{2} = \frac{ρ 2 l}{\frac{A}{2}} = \frac{4 ρ l}{A} n o w \frac{R_{1}}{R_{2}} = \frac{\frac{ρ l}{A}}{\frac{4 ρ l}{A}} = \frac{1}{4} \frac{2}{R_{2}} = \frac{1}{4} R_{2} = 8 o h m$

Suggest Corrections

Similar questions

2 L

R

a

l

R

o h m

4 a

Join BYJU'S Learning Program