Current Electricity 1 Question 2
2. A current of 5 A passes through a copper conductor (resistivity $=1.7 \times 10^{-8} \Omega-m$ ) of radius of cross-section 5 $mm$. Find the mobility of the charges, if their drift velocity is $1.1 \times 10^{-3} m / s$.
(2019 Main, 10 April I)
(a) $1.5 m^{2} / V-s$
(b) $1.3 m^{2} / V$-s
(c) $1.0 m^{2} / V-s$
(d) $1.8 m^{2} / V$-s
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Solution:
- Given,
$$ \begin{aligned} I & =5 A, \\ \rho & =1.7 \times 10^{-8} \Omega-m, \\ r & =5 mm=5 \times 10^{-3} m, \\ v _d & =1.1 \times 10^{-3} m / s \end{aligned} $$
Mobility of charges in a conductor is given by
$$ \mu=\frac{v _d}{E} $$
and resistivity is given by
$$ \begin{array}{rlrl} & \rho & =\frac{E}{J}=\frac{E}{I / A} \quad\left(\because J=\sigma E=\frac{1}{\rho} \times E\right) \\ \Rightarrow \quad & \rho & =\frac{E A}{I} \\ \text { or } \quad E & =\frac{\rho I}{A} \end{array} $$
From Eqs. (i) and (ii), we get
$$ \mu=\frac{v _d A}{\rho I} $$
Substituting the given values, we get
$$ \begin{aligned} & =\frac{1.1 \times 10^{-3} \times \pi \times\left(5 \times 10^{-3}\right)^{2}}{1.7 \times 10^{-8} \times 5} \\ & =\frac{86.35 \times 10^{-9}}{8.5 \times 10^{-8}}=10.1 \times 10^{-1} \Rightarrow \mu \approx 1 m^{2} / V-s \end{aligned} $$
