maths question

[kmatthews]

a capacitor of capacitive reactance 50ohms an inductor of 80 ohms inductive reactance and a resistor of 40 ohms are connected in series to a 200v 50hz supply the impedance will be:

the answer is 50ohms but i dont know the workings out.

anyone know how to do this.

cheers

 

[topquark]

Just to be sure, in series or parallel ?

 

[kmatthews]

series

think its got something to do with phasor angles?

 

[topquark]

I couldn't remember so did a bit of digging:

Here's the simple case with no resistance:
Series LC Circuits

and here's one with the resistance included:
Series RLC Circuits

In particular look at the effect on the voltage across the comps in the first example (not intuitive). Hope that helps.

Edit: I now feel the need to dig out my copy of horowitz and hill

 

[ericks]

a capacitor of capacitive reactance 50ohms an inductor of 80 ohms inductive reactance and a resistor of 40 ohms are connected in series to a 200v 50hz supply the impedance will be:

the answer is 50ohms but i dont know the workings out.
anyone know how to do this.
cheers

Hi there,
I hope this helps...

 

[pushrod]

Hi there,
I hope this helps...


View attachment 1437

Ericks is correct. It is a very standard question. Capacitive reactance and inductive reactance act in opposite directions to each other and so you just take the difference between them - in this case it is 30 ohms. You are then working out the third side of your impedance triangle, using pythagorus. You have R (40), X (30) and the hypotenuse of triangle is Z. It is very common to have these 3, 4, 5 triangles or multiples of eg 6, 8, 10; - 30, 40, 50; - 60, 0, 100 etc etc