Quick Formula Confirmation

[hightower]

I've a mock paper to do in preparation of my 202 exam. One of the questions is:

A circuit dissipates 7.5kW at a power factor of 0.9 when connected to a 230V a.c. supply. The current flowing in the circuit will be:

a) 13.0A
b) 29.3A
c) 21.5A
d) 25.2A


Now, this is where I might be loosing my mind.

Here are my calculations - can somebody confirm whether I'm wrong or the textbook is wrong.

a.c. Power = V * I * PF

therefore:

I = P / V * PF

I = 7500 / 230 * 0.9

I = 7500 / 207

I = 36.23A


Now, if you did it this way, you'd end up with answer B in the textbook:
I = (P / V) * PF

I = 32.6 * 0.9

I = 29.3A


However, if you re-enter those values into P = V * I * PF:

P = 230 * 29.3 * 0.9 = 6065W

Whereas if you enter my first values in:

P = 230 * 36.23 * 0.9 = 7499W



So am I going mad here and making a hash of my formulas or is the textbook wrong?

 

[hightower]

Furthermore to my reasoning, if the current at unity power would be 32.6A, surely the current with a poor power factor would be higher than 32.6A, not lower?

 

[telectrix]

oops. ...

 

[hightower]

oops. ...

I was about to say, isn't it kW / PF = kVA ?

 

[Simonslimline]

The textbook is wrong or i am also going mad?

 

[hightower]

The textbook is wrong or i am also going mad?

Thanks Simon, this is a C&G mock paper so it does have me second guessing my calculations.....

 

[Simonslimline]

I would say the current flowing is 36.23Amps.

 

[Pete999]

I've a mock paper to do in preparation of my 202 exam. One of the questions is:

A circuit dissipates 7.5kW at a power factor of 0.9 when connected to a 230V a.c. supply. The current flowing in the circuit will be:

a) 13.0A
b) 29.3A
c) 21.5A
d) 25.2A


Now, this is where I might be loosing my mind.

Here are my calculations - can somebody confirm whether I'm wrong or the textbook is wrong.

a.c. Power = V * I * PF

therefore:

I = P / V * PF

I = 7500 / 230 * 0.9

I = 7500 / 207

I = 36.23A


Now, if you did it this way, you'd end up with answer B in the textbook:
I = (P / V) * PF

I = 32.6 * 0.9

I = 29.3A


However, if you re-enter those values into P = V * I * PF:

P = 230 * 29.3 * 0.9 = 6065W

Whereas if you enter my first values in:

P = 230 * 36.23 * 0.9 = 7499W



So am I going mad here and making a hash of my formulas or is the textbook wrong?

KW / pf = X
X/230 = 29.3 I think

 

[hightower]

KW / pf = X
X/230 = 29.3 I think

That would equate to with the numbers put in:

7500 / 0.9 = 8333
8333/230 = 36.23

 

[Richard Burns]

I think they are being misdirectional in that the kVA of the circuit is 7.5 so the current is Va*pf/V =29.3A


On your calculations you are mixing the areas of division and multiplication.
I = P / V * PF looks OK in a straight line but if you multiply the volts by the PF then you have actually divided by pf not multiplied. For the equation rearrangement you need to multiply the top of the fraction by pf not the bottom.

Sorry not thinking at the moment. The KVa is kW/pf i.e is V*I /pf so (230*29.3)/0.9 =7500

 

[Pete999]

that would equate to with the numbers put in:

7500 / 0.9 = 8333
8333/230 = 36.23

7500 times 0.9

 

[hightower]

Here's an online calculator I've found, and I've entered the numbers exactly as they appear in the question, and using my calculated current of 36.23 the power factor is 0.9 which is as the question says. If I enter 29.3 in the current and click calculate it comes back as "power factor cannot be great than 1"

 

[hightower]

7500 times 0.9

But VA (Apparent Power) is bigger than W (True Power) when not at unity. Multiplying the True Power by the Power Factor gets a smaller result so surely this can't be right?

 

[hightower]

I'm fairly certain I've transposed my formulas the right way, but I've attached a photo of a different working, using a simple formula triangle like the same some people use to remember Ohm's Law formulas etc. Again, the answer comes back 36.23A

 

[happysteve]

kVA will always be greater than or equal to kW, because kVA is the hypotenuse (the long side, the one opposite the right angle) of the triangle.

The question says "dissipates" which means "consumes" or "uses up" or "turns into heat" 7.5kW of power... also the fact that it's in kW suggests that the intention of the question is that true power = 7.5kW.

If you're not sure whether apparent power (kVA) is (kW x pf) or (kW / pf), then try both... the one where you get a higher number is the correct one.

pf = kW / kVA <---- FACT

So kVA = kW / pf = 7.5 / 0.9 = 8.33kVA

So the current flowing is 8333 / 230 = 36.23A.

So it's the answers in the mock exam paper that are all wrong.

The correct answer is: "none of the above"

Where is the mock paper from, out of interest? Wouldn't be the first time someone's made an error in an exam paper...