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

Question

A nichrome wire 50 cm long and 1 mm 2 in cross-section carries a current of 4 A when connected to a 2 V storage battery. The resistivity of nichrome is (A) 1 × 10-6 Ω m (B) 2 × 10-7 Ω m (C) 4 × 10-7 Ω m (D) 5 × 10-7 Ω m

Tardigrade Admin · Accepted Answer

Here, l=50 cm =50 × 10-2 m A=1 mm 2=1 × 10-6 m 2, V=2 V, I=4 A According to Ohm's law, V=I R or R=(V/I)=(2/4)=(1/2) Ω...(i) Resistance of a wire is R=ρ (l/A) or ρ (l/A)=(1/2) (Using (i)) ∴ ρ=(A/2 l)=(10-6/2 × 50 × 10-2)=10-6 Ω m

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

$1 \times 1 0^{- 6} Ω m$

$2 \times 1 0^{- 7} Ω m$

$4 \times 1 0^{- 7} Ω m$

$5 \times 1 0^{- 7} Ω m$

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

1×10−6Ωm

2×10−7Ωm

4×10−7Ωm

5×10−7Ωm

Here, l=50cm=50×10−2m A=1mm2=1×10−6m2,V=2V,I=4A According to Ohm's law, V=IR or R=IV​=42​=21​Ω...(i) Resistance of a wire is R=ρAl​ or ρAl​=21​ (Using (i)) ∴ρ=2lA​=2×50×10−210−6​=10−6Ωm

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

$1 \times 1 0^{- 6} Ω m$

$2 \times 1 0^{- 7} Ω m$

$4 \times 1 0^{- 7} Ω m$

$5 \times 1 0^{- 7} Ω m$