What is the circuit impedance?

[Bradfoxthelegend]

Ran into this gem on the test:

A 199 volt, 60Hz AC voltage is put across a series circuit with an 8 ohm resistor and a capacitor who’s reactance is 15 ohms. What is the circuit impedance?
Your Answer: 23 ohms

The impedance is determined by finding the ohms. This question is poorly worded. Once in ohms the components just add together. If the numbers were adding in a complex form it would be 8<0 +15<-90 = 17<-61.9. This answer was not available and just "17" is not correct.

Am I wrong

[3Ashockers]

Ran into this gem on the test:

A 199 volt, 60Hz AC voltage is put across a series circuit with an 8 ohm resistor and a capacitor who’s reactance is 15 ohms. What is the circuit impedance?
Your Answer: 23 ohms

The impedance is determined by finding the ohms. This question is poorly worded. Once in ohms the components just add together. If the numbers were adding in a complex form it would be 8<0 +15<-90 = 17<-61.9. This answer was not available and just "17" is not correct.

Am I wrong


The impedance is the resultant "resistance" of pure resistance and reactance. Pythag theorem will give you your answer, 17. You can't add them together directly because, as you noted, they are at different phase angles. Since the they didn't ask for Z and resulting angle, I'm sure the correct answer was simply Z=17

Looking at it as vector algebra, they were only asking for the the magnitude, which would be a scalar and 17 ohms with no angle would be an acceptable answer.

Alternatively, even if you feel 17 isn't 100% correct it is MORE correct than 23 ohms.

[SuspectK]

Yeah, 17 is correct.

Square root(8*8 + 15*15)

http://www.datwiki.net/images2/Impedence-triangle.jpg
Remember, you need to convert capacitance and inductance into Ohms BEFORE you find the missing side of the Impedance right triangle, which this equation did a step for you by giving you the Xc value.

Capacitance- Xc= 1/2pie(3.1416)*f(Hz)* C(farads)
Inductance- XL= 2pie(3.1416)*f(Hz)* L(Henrys)