A copper wire has a diameter of 0 5 mm and resistivity of 1 6 × 10 8Ωm What - Science - Electricity

Question

A copper wire has a diameter of 0 5 mm and resistivity of
1 6 × 10 −8 Ω
m What has to be the length of this wire so that its
resistance becomes 10 Ω ? How much
will the resistance change if the diameter is doubled?tell the
length of wire?

Jyoti Pant · Accepted Answer

Solution: Here diameter of copper wire=0 5 mm radius=0 5/2=0 25mm= $0 25 \times 10^{- 3} m$ Area of cross section of wire= $π r^{2}$ = $\frac{22}{7} \times {0 25 \times 10}^{- 3} \times {0 25 \times 10}^{- 3}$ $Re s i s t i v i t y ρ = 1 6 \times 10^{- 8} Ω m Re s i s \tan c e R = 10 Ω l e n g t h = l (\sup p o s e) N o w ρ = \frac{R \times A}{l} p u t t i n g t h e v a l u e s, w e g e t 1 6 \times 10^{- 8} = \frac{10 \times 0 1964 \times 10^{- 6}}{l} l = \frac{10 \times 0 1964 \times 10^{- 6}}{1 6 \times 10^{- 8}} = 122 7 m T h u s t h e l e n g t h o f w i r e r e q u i r e d t o m a k e 10 Ω r e s i s \tan c e = 122 7 m N o w t h e r e s i s \tan c e o f w i r e i s i n v e r s e l y p r o p o r t i o n a l t o t h e ({d i a m e t e r)}^{2} s o w h e n d i a m e t e r i s d o u b l e d, r e s i s \tan c e w i l l b e c o m e {(\frac{1}{2})}^{2} o r \frac{1}{4} t h$

A copper wire has a diameter of 0.5 mm and resistivity of 1.6 × 10 −8 Ω m. What has to be the length of this wire so that its resistance becomes 10 Ω ? How much will the resistance change if the diameter is doubled?tell the length of wire?

A copper wire has a diameter of 0.5 mm and resistivity of 1.6 × 10 ⁻⁸ Ω m. What has to be the length of this wire so that its resistance becomes 10 Ω ? How much will the resistance change if the diameter is doubled?tell the length of wire?