Revision question

[stueelad]

Came across this question while doing some revision. I was hoping someone could help me to work it out.

A capacitor of capacitive reactance 5Ω, an inductor of 8 Ω inductive reactance and a resistor of 4 Ω are connected in series to a 230v 50 Hz supply. The total impedance of the circuit will be:

A - 4 Ω
B - 50 Ω
C - 40 Ω
D - 5 Ω

 

[Guest123]

My maths is a bit sketchy as it's been a while since I did a calc like this but thought I'd have a go to see if I could remember, I came up with the forumula Z = the sq root of Rsquared + (xl-xc)squared.

= sqroot of 4squared + 3squared = sqroot of 25 = 5ohms.


Like I say it's been a while so apologies if it's incorrect and I'm sure someone else will be along to correct me if it is.

 

[paturback]

Sounds right to me Lenny
Impedance is the algebraic sum of the separate load
values thus:
Z =√ (R2 + XL2) or√ (R2 + XC2)
If R, XL and XC are present in series in the same circuit
then XL and XC may be summated, treating XC as nega-
tive, thus
Z =√ (R squared + (XL - XC)squared)

 

[Guest123]

Nice one.

I sort of remembered that if both values appeared, as they would be 180 degrees apart i.e on the same line you would treat the xc as - & the xl as + thereby subtracting xc from xl.

Nice to know I havn't forgotten everything.

 

[paturback]

Yep thanks lenny I just remember it from when in series you just reminded me why..

Inductive reactance XL is proportional to the frequency and the inductance.

Capacitive reactance XC is inversely proportional to the frequency and the capacitance.