Question

Charge passing through a conductor of cross-section area $A=0.3 \,m ^{2}$ is given by $q=3 t^{2}+5 t+2$ in coulomb, where $t$ is in second. What is the value of drift velocity at $t=2 s ?$ (Given, $\left.n=2 \times 10^{25} / \,m ^{3}\right)$

• A. $0.77 \times 10^{-5} \,m/s$
• B. $1.77 \times 10^{-5}\, m/s$
• C. $2.08 \times 10^{-5}\, m/s$
• D. $0.57 \times 10^{-5} \,m/s$

Answer 1

The Correct Option is B

The correct option is(B): \(= 1.77\times 10^{-5} \,m/s\).

Given \(: A = 0.3 \,m^{2}\)
\(n = 2 \times10^{25}/m^{3}\)
\(q =3t^{2} + 5t +2\)
\(i= \frac{dq}{dt} = 6t +5 = 17\)
\(i=n e A v_{d}\)
Drift velocity, \(v_{d} = \frac{i}{neA}\)
\(= \frac{17}{ 2\times 10^{25} \times 1.6\times 10^{-19}\times 0.3 }\)
\(= \frac{17}{0.96\times 10^{6}}\)
\(= 1.77\times 10^{-5} \,m/s\)