in this video we're going to focus on the series RLC circuit so in this example we have a capacitor that is in series with an inductor a resistor and an AC signal so let's draw a circuit so here's the resistor here's the inductor and here's the capacitor so we have a 30 M resistor a 100 milli Henry inductor and a 40 micro farad capacitor and we have a 15 vote 60 Hertz AC signal so let's focus on Part A calculate the capacitive reactance in the circuit so here's the formula for capacitive reactance it's 1 divided by 2 pi FC F is the frequency which is 60 Hertz and C is the capacitance which is 40 micro farad or 40 times 10 to the minus 6 ference and so the capacitive reactance XC is sixty six point three ohms now let's move on to the second part of Part II so now let's calculate the inductive reactance represented by the symbol Excel and that's equal to 2 pi F M so the inductance L is a hundred milli henries so that's a hundred times 10 to minus 3 Henry's and so X L is thirty seven point seven ohms so now that we have the capacitive reactance and we have the inductive reactance let's go ahead and calculate the impedance in a circuit represented by the letter Z and so here's the formula for it it's R squared plus XL minus XC squared in this example are the resistance is 30 ohms the inductive reactance is thirty seven point seven ohms and the capacitive reactance is sixty six point three ohms so go ahead and type that in so the impedance in the in circuit it's forty one point four five ohms and so that's how you can calculate the impedance if you have a series RLC circuit Part C calculate the RMS current and the circuit so we can use this formula the voltage is equal to the RMS current times the impedance so the RMS current in the circuit is going to be the voltage of the source that is the fifteen volt AC signal divided by the impedance so it's 15 divided by forty one point four five ohms and so the current is point three six one nine amps so that's the RMS current that flows in a circuit now let's move on to Part D calculate the voltage across the resistor the inductor and the capacitor so let's start with a resistor so V is equal to IR but we're going to use the RMS current so it's gonna be 0.36 one nine times the resistance of 30 ohms and so the voltage across this resistor is going to be ten point eight five seven volts now let's do the same thing with the inductor the voltage across the inductor is going to be the current times the capacitive I mean the inductive reactance so that's gonna be 0.36 1-9 x XL which is thirty seven point seven ohms and so VL in this example is thirteen point six four four volts now let's calculate the voltage across the capacitor so it's going to be the current multiplied by the capacitive reactance which is sixty six point three and so the voltage across the capacitor is twenty three point nine nine four volts so now you know how to calculate the voltage across the resistor the inductor and a capacitor and to check your answer you could use this formula so V s should be equal to the square root of V R squared plus VL minus v/c squared so V R is ten point eight five seven squared VL that's thirteen point six four four VC is twenty three point nine nine four go ahead and type that in see what you get this should give you fourteen point nine nine nine nine volts which matches the voltage of the source so that's how you know if you have the right voltages in this example Part II how much power is consumed in the circuit only the resistor consumes energy so the power absorbed by the resistor is the power absorbed by the entire circuit that the pass for any inductor they absorb energy but they give it back to the circuit so we don't have to worry about those two elements the current in the circuit that's 0.36 1:9 and the resistance is 30 and so this is going to be three point nine to nine watts now we can confirm this answer with another formula so the power consumed in the circuit it's also the RMS voltage of the source multiplied by the RMS current of the source times the power factor the power factor is the resistance divided by the impedance now the resistance of the circuit is thirty and the impedance is forty one point four five so the power factor is point seven two three eight so now let's use this formula so the voltage of the AC signal that's fifteen volts multiplied by the RMS current of 0.36 one nine multiplied by the power factor of 0.7 two three eight and so this will give you the same answer of 3.9 to 9 watts so you have two ways in which you can calculate the power consumed by the circuit now what about the last part what is the resonant frequency of the circuit the formula that will help us to calculate it into 1/2 pi times the square root of LC and so L in this example is a hundred milli henries so that's point one Henry's and the capacitance it's 40 micro farad's or 40 times 10 to the minus 6 and so the resonant frequency and this example is seventy nine point six Hertz which is not too far off from sixty now at this frequency excel is equal to XC the inductive reactance and the capacitive reactance they equal each other so in this formula where the impedance is R squared plus X L minus XC squared when X L equals XE XL minus XC becomes zero so then Z becomes the square root of R squared which in this case Z is equal to R so at the resonant frequency these two values will be equal right now you can see that they're close at 60 but at seventy nine point six these two are equal and the impedance is equal to the resistance of the circuit