A nichrome wire 50 cm long and 1 mm2 cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of nichrome wire is

Question

A nichrome wire 50 cm long and 1 mm2 cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of nichrome wire is (A)  1× 10-6 Ω -m  (B)  4× 10-7 Ω -m  (C)  .3× 10-7 Ω -m  (D)  2× 10-7 Ω -m

Tardigrade Admin · Accepted Answer

Here, l=50 cm =0.5 m and A=1 mm 2=10-6 m 2 As R=(V/i)=(ρ l/A) ⇒ ρ=(V A/i l) =(2 × 10-6/4 × 0.5)=10-6 Ω- m =1 × 10-6 Ω- m

Q. A nichrome wire $50 c m$ long and $1 m m^{2}$ cross-section carries a current of $4 A$ when connected to a $2 V$ battery. The resistivity of nichrome wire is

$1 \times 1 0^{- 6} Ω - m$

$4 \times 1 0^{- 7} Ω - m$

$.3 \times 1 0^{- 7} Ω - m$

$2 \times 1 0^{- 7} Ω - m$

Here, $l = 50 c m = 0.5 m$
and $A = 1 m m^{2} = 1 0^{- 6} m^{2}$
As $R = \frac{V}{i} = \frac{ρl}{A}$
$\Rightarrow ρ = \frac{V A}{i l}$
$= \frac{2 \times 1 0 ^{- 6}}{4 \times 0.5} = 1 0^{- 6} Ω - m$
$= 1 \times 1 0^{- 6} Ω - m$

Q. A nichrome wire 50cm long and 1mm2 cross-section carries a current of 4A when connected to a 2V battery. The resistivity of nichrome wire is

1×10−6Ω−m

4×10−7Ω−m

.3×10−7Ω−m

2×10−7Ω−m