The jigsaw can be used to make both straight and curved cuts in a wide variety of materials, including wood, particleboard, plywood, plastic, metal, even ceramic tile. There is also way more than those, but those are just the basics or common things. Hope this helps!
Complete Question
An aluminum "12 gauge" wire has a diameter d of 0.205 centimeters. The resistivity ρ of aluminum is 2.75×10−8 ohm-meters. The electric field in the wire changes with time as E(t)=0.0004t2−0.0001t+0.0004 newtons per coulomb, where time is measured in seconds.
I = 1.2 A at time 5 secs.
Find the charge Q passing through a cross-section of the conductor between time 0 seconds and time 5 seconds.
Answer:
The charge is ![Q =2.094 C](https://tex.z-dn.net/?f=Q%20%3D2.094%20C)
Explanation:
From the question we are told that
The diameter of the wire is ![d = 0.205cm = 0.00205 \ m](https://tex.z-dn.net/?f=d%20%3D%20%200.205cm%20%3D%200.00205%20%5C%20m)
The radius of the wire is ![r = \frac{0.00205}{2} = 0.001025 \ m](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B0.00205%7D%7B2%7D%20%3D%200.001025%20%20%5C%20m)
The resistivity of aluminum is ![2.75*10^{-8} \ ohm-meters.](https://tex.z-dn.net/?f=2.75%2A10%5E%7B-8%7D%20%5C%20ohm-meters.)
The electric field change is mathematically defied as
![E (t) = 0.0004t^2 - 0.0001 +0.0004](https://tex.z-dn.net/?f=E%20%28t%29%20%3D%20%200.0004t%5E2%20-%200.0001%20%2B0.0004)
Generally the charge is mathematically represented as
![Q = \int\limits^{t}_{0} {\frac{A}{\rho} E(t) } \, dt](https://tex.z-dn.net/?f=Q%20%3D%20%5Cint%5Climits%5E%7Bt%7D_%7B0%7D%20%7B%5Cfrac%7BA%7D%7B%5Crho%7D%20E%28t%29%20%7D%20%5C%2C%20dt)
Where A is the area which is mathematically represented as
![A = \pi r^2 = (3.142 * (0.001025^2)) = 3.30*10^{-6} \ m^2](https://tex.z-dn.net/?f=A%20%3D%20%20%5Cpi%20r%5E2%20%3D%20%20%283.142%20%2A%20%280.001025%5E2%29%29%20%3D%203.30%2A10%5E%7B-6%7D%20%5C%20m%5E2)
So
![\frac{A}{\rho} = \frac{3.3 *10^{-6}}{2.75 *10^{-8}} = 120.03 \ m / \Omega](https://tex.z-dn.net/?f=%5Cfrac%7BA%7D%7B%5Crho%7D%20%3D%20%20%5Cfrac%7B3.3%20%2A10%5E%7B-6%7D%7D%7B2.75%20%2A10%5E%7B-8%7D%7D%20%3D%20%20120.03%20%5C%20m%20%2F%20%5COmega)
Therefore
![Q = 120 \int\limits^{t}_{0} { E(t) } \, dt](https://tex.z-dn.net/?f=Q%20%3D%20120%20%5Cint%5Climits%5E%7Bt%7D_%7B0%7D%20%7B%20E%28t%29%20%7D%20%5C%2C%20dt)
substituting values
![Q = 120 \int\limits^{t}_{0} { [ 0.0004t^2 - 0.0001t +0.0004] } \, dt](https://tex.z-dn.net/?f=Q%20%3D%20120%20%5Cint%5Climits%5E%7Bt%7D_%7B0%7D%20%7B%20%5B%200.0004t%5E2%20-%200.0001t%20%2B0.0004%5D%20%7D%20%5C%2C%20dt)
![Q = 120 [ \frac{0.0004t^3 }{3} - \frac{0.0001 t^2}{2} +0.0004t] } \left | t} \atop {0}} \right.](https://tex.z-dn.net/?f=Q%20%3D%20120%20%5B%20%5Cfrac%7B0.0004t%5E3%20%7D%7B3%7D%20-%20%5Cfrac%7B0.0001%20t%5E2%7D%7B2%7D%20%2B0.0004t%5D%20%7D%20%20%5Cleft%20%7C%20t%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
From the question we are told that t = 5 sec
![Q = 120 [ \frac{0.0004t^3 }{3} - \frac{0.0001 t^2}{2} +0.0004t] } \left | 5} \atop {0}} \right.](https://tex.z-dn.net/?f=Q%20%3D%20120%20%5B%20%5Cfrac%7B0.0004t%5E3%20%7D%7B3%7D%20-%20%5Cfrac%7B0.0001%20t%5E2%7D%7B2%7D%20%2B0.0004t%5D%20%7D%20%20%5Cleft%20%7C%205%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
![Q = 120 [ \frac{0.0004(5)^3 }{3} - \frac{0.0001 (5)^2}{2} +0.0004(5)] }](https://tex.z-dn.net/?f=Q%20%3D%20120%20%5B%20%5Cfrac%7B0.0004%285%29%5E3%20%7D%7B3%7D%20-%20%5Cfrac%7B0.0001%20%285%29%5E2%7D%7B2%7D%20%2B0.0004%285%29%5D%20%7D)
![Q =2.094 C](https://tex.z-dn.net/?f=Q%20%3D2.094%20C)