Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery.

a. What is the capacitance?

Video transcript

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A pair of copper electrodes each with a diameter of 4.0 centimeters are separated by 0.70 millimeters. What is their capacitance if these elect roads are connected to a 200 volt power supply? So that's our goal. Our angle is we're trying to figure out what the capacitance is of this particular pair of copper electrodes. And that's our final answer that we're ultimately trying to solve for. Now, let's look over our multiple choice answers to see what our final answer might be. And let us note that they're all in units of fads. So A is 1.6 multiplied by 10 to the power of negative 11 B is 2.3 multiplied by 10 to the power of negative 11 C is 4.4 multiplied by 10 to the power of negative 11 and D is 5.2 multiplied by 10 to the power of negative 11. So first off, let us write down all of our given variables or all of our known variables to be precise. So we know that the diameter of each electrode, so let's call the diameter capital D is equal to 4.0 centimeters, which is also equal to zero 0.04 m. So you can use dimensional analysis to perform this conversion or you could quickly look it up. I've just given it to you to save some time in our solving process. Here. We also know that the separation distance which is the separation between the electrodes. We're gonna call this value. Lower case D is equal to 0.70 millimeters, but we need to convert millimeters to meters. So 0.0007 m and we also know that the voltage V is equal to 200 volts. Awesome. So now our next step is we need to calculate the area which we're in a denote area as capital a of one electrode. So we need to recall and use our area equation which states that A is equal to pi multiplied by D divided by two square. So the area of one electrode is equal to pi multiplied by D divided by two square. So now we could plug in all of our known variables and solve for A. So we know that A is equal to pi multiplied by our capital D diameter which is 0.4. So, so it's 0.04 m divided by two squared. So let me plug that into our calculator. We will find that A is equal to 1.256637 multiplied by 10 to the power of negative three meters squared. So now our next step which we're finally able to solve for the capacitance capital C, which is our final answer that we're ultimately trying to solve for. So in order to find the capacitance, we had to find the area first. So now when we go to calculate the capacitance C by using the formula for a parallel plate capacitor, which we should be able to recall that this equation is for a parallel plate capacitor states that the capacitance C is equal to epsilon zero multiplied by capital A divided by lowercase D where epsilon zero is our permittivity of free space constant. So now we could plug in all of our known variables to solve for C our final answer. So as we should recall epsilon zero, we should know that that value the constant is equal to eight point 854 multiplied by 10 to the power of negative 12. And its units are fads per meter. And we need to multiply this value by our value of A which we just determined to be 1.256637 multiplied by 10 to the power of negative 3 m squared divided by our distance separation distance, which is 0.0 0.0007 m. Awesome. So when we plug that into our calculator, we will find that the capacitance C is equal to 1.58 946 multiplied by 10 to the power of negative 11 fa which is approximately equal to 1.6 multiplied by 10 to the power of negative 11 there at when we round to one decimal place. And that is our final answer. Hooray, we did it. So looking at our multiple choice answers, the correct answer is the letter A 1.6 multiplied by 10 to the power of negative 11 fads. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.