The number density of free electrons in a cop | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The relationship between current $I$ and drift velocity $v_d$ is given by $I = n A v_d e$,where $n$ is the number density,$A$ is the cross-section

Vedclass · Accepted Answer

$5.4 	imes 10^4 \ s$

Vedclass · Answer

(B) The relationship between current $I$ and drift velocity $v_d$ is given by $I = n A v_d e$,where $n$ is the number density,$A$ is the cross-sectional area,and $e$ is the elementary charge.Since $v_d = \frac{l}{t}$,where $l$ is the length of the wire and $t$ is the time taken,we can write:$I = n A \left( \frac{l}{t} ight) e$Rearranging for $t$:$t = \frac{n A l e}{I}$Given values:$n = 8.5 	imes 10^{28} \ m^{-3}$$A = 1.0 	imes 10^{-6} \ m^2$$l = 6 \ m$$e = 1.6 	imes 10^{-19} \ C$$I = 1.5 \ A$Substituting these values:$t = \frac{8.5 	imes 10^{28} 	imes 1.0 	imes 10^{-6} 	imes 6 	imes 1.6 	imes 10^{-19}}{1.5}$$t = \frac{81.6 	imes 10^3}{1.5} = 54.4 	imes 10^3 \ s$$t = 5.44 	imes 10^4 \ s$Thus,the correct option is $B$.

Similar Questions

$A$ current of $10 \,A$ is maintained in a conductor of cross-section $1 \,cm^2$. If the number density of free electrons is $9 \times 10^{28} \,m^{-3}$,the drift velocity of free electrons is .......... $m/s$.

There are $0.8 \times 10^{23}$ free electrons $/ cm^3$ in copper. If a $0.2 \, A$ current is flowing in a copper wire, then the drift velocity of electrons will be, given the cross-sectional area of the wire is $0.01 \, cm^2$.

Write Ohm's law in the form of current density (vector form).

$A$ copper wire of length $1\, m$ and radius $1\, mm$ is joined in series with an iron wire of length $2\, m$ and radius $3\, mm$ and a current is passed through the wires. The ratio of the current density in the copper and iron wires is

$A$ constant electric current $I$ is passed through a straight conductor of length $l$. If $S$ is the specific charge of an electron,then the total momentum of the electrons is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module