Charge passing through a conductor of cross-s | vedclass

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(B) Given: Area $A = 0.3 \,m^2$,charge density $n = 2 	imes 10^{25} / m^3$,and charge $q = 3t^2 + 5t + 2$.First,calculate the current $i$ at $t = 2 \

Vedclass · Accepted Answer

$1.77 	imes 10^{-5} \,m / s$

Vedclass · Answer

(B) Given: Area $A = 0.3 \,m^2$,charge density $n = 2 	imes 10^{25} / m^3$,and charge $q = 3t^2 + 5t + 2$.First,calculate the current $i$ at $t = 2 \,s$ using $i = \frac{dq}{dt}$.$i = \frac{d}{dt}(3t^2 + 5t + 2) = 6t + 5$.At $t = 2 \,s$,$i = 6(2) + 5 = 17 \,A$.The relationship between current and drift velocity $v_d$ is $i = n e A v_d$,where $e = 1.6 	imes 10^{-19} \,C$.Rearranging for $v_d$: $v_d = \frac{i}{n e A}$.Substituting the values: $v_d = \frac{17}{2 	imes 10^{25} 	imes 1.6 	imes 10^{-19} 	imes 0.3}$.$v_d = \frac{17}{0.96 	imes 10^6} = 17.708 	imes 10^{-6} \,m/s = 1.77 	imes 10^{-5} \,m/s$.

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,$n=2 \times 10^{25} / m^3$ )

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