Frequency question

[Lainge]

Hi all. Happy new year.

I am currently revising for my 301 exam, using the Advanced electrical installation book, but strugle to find any formula to get this correct answer, other than alter the frequencies of my XC & XL calculation until they are equal.

The question:

A circuit is made up of an inductor, a resistor and a capacitor all wired in series. When the circuit is connected to a 50hz a.c. suppl, a current of 2.2A flows. A voltmeter connected to each of the components in turn indicates 220vd across the inductor of 0.318H, 200v across the resistor & 180v accross the capacitor 38.9f.

The question: at what frequency would the capacitor and the inductor have the same reactance value (Neglect the resistance of the inductor)

 

[septiclecky]

Transpose the formulas for Xl or Xc so that the answer = f

 

[Lainge]

Would you mind explaining please as I can transpose but am strugling to grasp this question? Were not trying to find f were trying to work out at what Frequency both XC and XL are equal?

 

[Chr!s]

Hi lainge

The question:A circuit is made up of an inductor, a resistor and a capacitor all wired in series. When the circuit is connected to a 50hz a.c. suppl, a current of 2.2A flows. A voltmeter connected to each of the components in turn indicates 220vd across the inductor of 0.318H, 200v across the resistor & 180v accross the capacitor 38.9f.

Firstly find the value of xl and xc

Frequency affects inductance and capacitance inversely, xl + xc/2

Transpose the formula

F= xl + xc/2 divided by 2 x 3.142 x h

 

[Chr!s]

Well capacitance and inductance are inversely affected by frequency.

First i would find the value of Xc and Xl

So Xl = 100 ohms(220/2.2) Xc = 81.8182 (180/2.2 ) so Xl - Xc = 18.1818 divide by 2 = 9.0909

transpose formula for XL

9.0909 / 2 x 3.142 x .318 = 4.5493

50 Hz - 4.5493 Hz = 45.4507

so

Xl = 2 x 3.142 x 45.4507 x .318 = 90.82

Xc = 1/ 2 x 3.142 x 45.4507 x 38.9 x 10(po)-6 = 90.0064

So Frequency would need to 45 Hz to achieve same reactance.

 

[BS3036]

Capacitive reactance Xc = 1/(2*pi*f*C)

Inductive reactance Xl = 2*pi*f*L

if these are equal:

1/(2*pi*f*C) = 2*pi*f*L

so 4*pi*pi*f*f*L*C = 1

so f = SQRT(1/L*C) * 1/(2*pi)

= SQRT (1/(.318 * 38.9)) * 1/(2*pi)

= 0.0452 Hz

 

[Chr!s]

Lainge

Now have to hand my old level 3 book and with it a more simplified example than my first lol.

Fo = 1/(2 x Pi) X by sqrt(1/LC)Hz

So

1/ 2 x 3.142 = .159 ___X_____sqrt(1/ .318 x 38.9 x 10-6)= 284.322

.159 x 284.323 = 45.21 Hz

Not quite as long winded as my first example lol

 

[BS3036]

Plumber: You seem to be assuming the capacitor value is in uF, whereas it is stated in the OP to be in Farads.

 

[septiclecky]

Plumber: You seem to be assuming the capacitor value is in uF, whereas it is stated in the OP to be in Farads.

Jesus thats a large capacitor

 

[Chr!s]

Jesus thats a large capacitor

:^O

 

[Doc Hudson]

Plumber: You seem to be assuming the capacitor value is in uF, whereas it is stated in the OP to be in Farads.

As Plumber & Septiclecky suggest, I think that is an oversight by the OP, especially due to the unit values involved. However it raises an interesting point. If this had been an exam question, long hand written exam not multi-choice, with a similar error on the exam question, would you be expected to make reasonable assumption of the correct units, or just answer the question purely on the details given?

Doc H.

 

[BS3036]

Generally, after the examiners realise their error, both answers would be given credit.