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Welcome to a lecture online and here we have another example of how to use impedance in the calculations that we learn how to do with a parallel branch system now this case we're going to have three parallel branches Z 1 Z 2 and Z 3, and so we know that the total or 1 over the total impedance is equal to 1 over Z 1 plus 1 over Z 2 plus 1 over Z 3 and these are the three impedance we're going to work with so how do we do that again we cannot just do a simple vector kind of addition where we take all the real parts and all the imaginary parts and add them together because they're not in series they're in parallel there's a different method of doing that so let me go ahead and plug that into the equation over there, and then we'll figure out how to solve a problem like this all right, so this is equal to 1 over Z 1 and Z 1 is going to be 40 ohms with an angle of 60 degrees, and you know what I'm going to leave the ohm symbol off because that just makes a lot cleaner, so we'll just write 40 and an angle of 60 degrees plus 1 over that's going to be 80 with an angle of 20 degrees plus 1 over that's going to be 50 with an angle of minus 50 degrees now to put things in perspective whenever you have a positive angle it probably has to do with an inductive type branch, so the inductive properties of these two branches are bigger than the capacitive properties those branches therefore we have a positive angle, but the third branch right there definitely acts like a capacitive branch we have more capacitance and inductance, and so we have a negative angle there a negative reactive angle all right the first thing we're going to do is move those to the top and so 140 well that's equal to 148 with a new phase angle of minus 60 degrees so when we take the inverse it's like dividing one by the denominator you can think of the numerator as being a zero-degree angle that would be a zero-degree angle and a zero-degree angle so that when you divide one divided by 40 get 140th and when divided this angle by this angle you simply subtract angle 0-60 is minus 60 degrees same over here that would be plus one over 80 and an angle would be -20 degrees because 0 minus 20 is minus 20 and here plus 1 58 times an angle of plus 50 in this case excuse me plus 50 in this case because it's 0 minus a minus 50 becomes a plus 50, so now we have this all in the numerator now we simply have to add these together well we can't add them together in this format we now have to convert them to the complex number format, so we can add all the real parts and all the imaginary parts together, so we have a magnitude of 148 and an angle of 60 degrees so how do we get the real and imaginary parts well remember that the real part R is equal to EP Dan's the magnitude impedance times the cosine of the angle theta and to find the imaginary part X you get the magnitude of Z times the sine of theta so what this then becomes this would be equal to I'm going to give myself a little more room, so I'm...
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