In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0-m length of this wire.

Video transcript

Hi everyone. Today we are going to determine the resistance of a 1.2 kilometer long aluminum solid wire which will have a diameter of 2.91 millimeter. And in this case we are going to first start with just converting all the known dimensions of the wire into S. I units. So first we have the diameter which is 2. millimeter. Or in this particular example it's going to be 2. times 10 to the power of -3 m. The radius is going to be half a diameter And the radius itself is then going to be 1.45, 5 times 10 to the power of minus three m. Okay, so the length is given to be 1.2 kilometer, which in meter is going to be 1.2 times 10 to the power of three m. In this problem we are going to use the equation R equals rho L over A Where the RSR assistance. The row is the receptivity of the aluminum cable. The L. Is going to be the length and the A. Is going to be the cables, cross sectional area. So in this, in a normal cylindrical cable, the A. Is going to be pi multiplied by r squared where r is the radius of the cable. Okay, and then next, what we need to know is for aluminum, the resistive. Itty row is going to be 2. times 10 to the power of minus eight home multiplied by meter. And now we can actually start solving this problem because we we know all the values needed to calculate the resistance. So let's use this formula right here are real equals to rho multiplied by L. Divided by a. The row is 2.75 times 10 to the power of minus eight. Ro zero m. The L is 1.2 times 10 to the power of three m. And this will all be divided by pi multiplied by r square which is 1.455 times 10 to the power of minus three m square, just like so. Okay, so this will actually come out to be 4.96 pump and that is going to be our answer here, which is going to correspond to option C here. So the resistance of a 1.2 kilometer long strand of aluminum wire with a diameter of 2.91 millimeter is 4.96. And if you guys have any more confusion on this particular topic, please check out our other lesson videos regarding this particular topic and that will be all for this problem. Thank you.