What are the Components of a Circuit?

[WhiteTrout]

Homework Statement

A circuit contains two elements which are either L, R or C. The current in the circuit lags the source by 50 degrees when connected to a 120V, 60 Hz and i= 5.6A source.

Homework Equations

tan Φ = X/R
X= wL
R= V/I

The Attempt at a Solution

(The question does not give the structure of the circuit)
Given that the current lags by 50 degrees, then one element could be an inductor, L.
Upon assumption that the current in an LC circuit would be opposite and 180 degrees to each other, then

The circuit might be an LR circuit,

R= 21.428 ohm

if L= (R tan Φ)/w

then L= 0.06774 H

Logical?

 

[tiny-tim]

Welcome to PF!

Hi WhiteTrout! Welcome to PF!

I think for this question it would be clearer to use impedance rather than resistance and reactance …

each component's impedance will be a positive multiple of 1 j or -j …

which combination gives you a total impedance corresponding to current lagging by 50°? ​

 

[WhiteTrout]

Thank you for the warm welcome tiny-tim

The current lags so I suppose
Φ= -50 degrees (?)
If |Z| cos Φ + j|Z| sin Φ = R + jX

let
|Z| cos Φ = R
|Z| = 33.336 ohm (?)

then if
j|Z| sin Φ = jX
jX = -25.5368 j

Therefore, j= -j (?)

I'm sorry, but the idea wasn't covered in my syllabus so I tried to gather what I could from the PF library entry and applied it; I have no idea if what I did is correct

But please do drop more hints. I'm quite eager to see this one out.

Thank you.

 

[tiny-tim]

Hi WhiteTrout!

The current lags so I suppose
Φ= -50 degrees (?)

No, Φ is the phase difference by which the voltage leads the current.

General rule:

If we have a resistor R an inductor L and a capacitor C in series in an AC circuit,

then the voltage drops are R ωLj and -(1/ωC)j [= (1/ωCj)] times the current

(and the total voltage drop is the sum).

So if (as in this case) you want the total to be A + Bj times current, with both A and B positive,

then you clearly need more L than C (and if you're only allowed two items, that means no C). ​

 

[WhiteTrout]

Sorry for the late reply.

No, Φ is the phase difference by which the voltage leads the current.

Aha. That clears it up a lot. Thank you.

Okay I see the picture better now.

L is the component that will give Φ= 90 degree when under a pure inductive load.
And to have Φ<90 we would have to include R as one of the component.

Is that right? So it means that in this case, it would have to be an LR circuit.

So if 3 components are included, that means that L>C; because otherwise it'll give us Φ= -ve.

Out of curiosity, in an LC circuit, does it mean that Φ can only be Φ= +90/-90 depending on which component has the bigger impedance?

Thank you tiny-tim.

 

[tiny-tim]

Out of curiosity, in an LC circuit, does it mean that Φ can only be Φ= +90/-90 depending on which component has the bigger impedance?

Yes.

(except I think that's purely theoretical … there'll always be some resistance, both in the wiring and in the battery itself )

Of course, it will depend on ω …

but if you choose L C and ω exactly right, the impedance will be purely real (the reactance is zero), and the LC combination will behave as purely resistive (I think that's called resonance).

 

[WhiteTrout]

Oh okay, I see it.

Thank you for helping me through this topic tiny-tim. :)
I'm glad to walk off with a better understanding now.

also, apologies for the late reply.