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Electric Circuits 9th Edition Solutions
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hey all it's bekah I'm a math physics and astronomy tutor here at Chegg if you ever need such a tutor feel free to hit me up on my profile which is linked below but today I'm going to talk to you all about conductivity now conductivity is a way that we measure the likelihood of having current flow through a material it's a concept that you've probably heard of if you're in physics too if you're in a material science course or if you're tangled taking electricity and magnetism or something like that conductivity is associated with circuits and electric current and things like that so conceptually and mathematically it is the opposite of resistivity which is the ability of a material to resist current flowing through it so conductivity is the opposite of that it's the ability of a material to allow current to flow through it so conductivity is given as the Greek letter or lowercase Sigma which I draw like that um and resistivity is given by the Greek letter Rho which I draw like that so if you would like to find the conductivity of a material you would simply take the reciprocal or the opposite of the resistivity so how do we do that if we have this slab of material right here that has an internal resistance of 2 ohms a length of 20 centimeters here and a width of 10 centimeters right here now you may recall if you've ever had to calculate resistivity before or resistance from resistivity that resistivity is equal to the internal resistance times the cross-sectional area which is the square right here in this material divided by the length of material we're considering right here so from resistivity we can find conductivity so let's say we want to find the conductivity of this material right here well we have the internal resistance with which is 2 ohms and we have length and we have width of these sides of the square here but we know that an SI unit our resistance units should be ohms and that's fine that's what we have but our distance unit should be in meters so 20 centimeters is two-tenths of a meter or 0.2 meters and likewise width 10 centimeters is one-tenth or point 1 meters okay so since we know that this is a square the width and the width are the side lengths of a square we can find the cross-sectional area as being point 1 times point 1 or area of a square 0.1 squared + 1 x squared is just 1 100 so we have 0.01 square meters okay now we have everything that we need to find the resistivity of this material so resistivity is equal to the internal resistance which we have 2 ohms times the area we have 0.01 meters squared and divided by the length we have zero point two meters alright so dimensionally please see that we have meter squared on top and meters on the bottom so one of those meters is going to cancel out and our final unit of resistivity is going to be ohms times meters or 0 meters okay and 2 points 2 times point 0 1 0 is point 0 2 point 0 2 / point2 is simply 0.1 or one-tenth Oh meters but our final answer is not resistivity but it is productivity so now that we have the resistivity we can plug this into our conductivity equation and we know that conductivity Sigma is equal to one divided by zero point 10 meters and 1/10 is simply 10 and we can write that in inverso meters okay so this is how to find the conductivity of a material which again is the likelihood of current to flow through the material the opposite of resistivity hope this helps you all out if you need any assistance with your en on problems feel free to hit me up or any other physics tutor here on Chegg okay hi guys
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