Question

In an integrated circuit, the current density in a $2.5m-thick\times 75\mu m-wide$wide gold film is localid="1648893767234" $7.5\times {10}^5\mathrm{A}/{\mathrm{m}}^2$. How much charge flows through the film in $15\min$?

Short answer

The amount of charge flows through the film in$15min$is$0.127C.$

Step-by-step solution

Given Information

Integrated circuit thickness$=2.5m$

Integrated circuit wide$=75\mu m$

Current density$=7.5\times {10}^5\mathrm{A}/{\mathrm{m}}^2$

Time$=15min$

Explanation

Using the latter's definition of the intensity, we can express the charge passed through time as follows:

$I:=\frac{Q}{t}\Rightarrow Q=It$

The current can be found from the current density and the area of the cross-section as follows:

$J:=\frac{I}{A}\Rightarrow I=JA$

Substituting, we have

$Q=JAt$

Since the cross-section is a rectangle, let us substitute it's an area, thus finding

$Q=Jabt$

Substitute the expression,

localid="1648894401072" role="math" $Q=(7.5\times {10}^{5}A/m^2\times 2.5\times {10}^{-6}m\times 7.5\times {10}^{-5}A/m^2\times 15s\times 60s)$

Simplify the expression,

$=0.127\mathrm{C}$

Final Answer 

Hence, the amount of charge flows through the film in $15min$is$0.127C$