### Current Electricity Question 5

#### Question 5 - 25 January - Shift 1

A uniform metallic wire carries a current $2 A$. when $3.4 V$ battery is connected across it. The mass of uniform metallic wire is $8.92 \times 10^{-3} kg$. density is $8.92 \times 10^{3} kg / m^{3}$ and resistivity is $1.7 \times 10^{-8} \Omega-m$. The length of wire is :

(1) $l=6.8 m$

(2) $l=10 m$

(3) $l=5 m$

(4) $l=100 m$

## Show Answer

#### Answer: (2)

#### Solution:

$I=2 A$

$\Delta V=3.4 V$

Using Ohm’s Law

$R=\frac{3.4}{2}=1.7 \Omega$

$1.7=\frac{\rho L}{A}$

$L=\frac{1.7(A)}{\rho}$

$M=($ density volume $)$

Volume $=\frac{8.92 \times 10^{-3}}{8.92 \times 10^{3}}=10^{-6}$

$L^{2}=\frac{1.7}{\rho}(10^{-6})=\frac{1.7}{1.7} \times 10^{2}$

$L=10 m$