Hi,

Can someone please help me with this problem?

A 60-cycle/sec source of emf is impressed across a series circuit consisting of a 10-ohm resistance and a capacitance of unknown value.
Rms voltage is 100 volts and rms current is 0.2 amperes.

Calculate
a) the impedance of the circuit,
b) the power consumption,
c) the power factor,
d) the value of capacitance

 

You should be putting these in the homework section.

 

This LCR circuit doesn't have an "L". Maybe the question should go in a Christmas homework section? (No L, No L, No L, No L. Born is the King...)

 

Ok, I think we have to assume no XL-value in the circuit.

Can we start to say that Z = Urms/ Irms = 500ohms

That gives a too high XC-value compared to R.

Some suggestion on a better way to do it?

 

That gives a too high XC-value compared to R.

Does it? Show your calculation and your cross checking.

 

Why do you think that is incorrect?

 

Z = ((R^2 -(XL -XC))^2 )^1/2

Assumes that XL is 0.

500= (100 - XC^2)^1/2

250000 = 100 - XC^2

XC = 500,1

This is incorrect. Can someone please help me?

 

Bacause I haven't taken the power factor into account.

 

You haven't solved the power factor question yet ....

Why did you delete your post with the answer of 499.9 and change it to 500.1? You went from close answer, as you rounded it to one decimal place to an incorrect answer.

 

Z = ((R^2 -(XL -XC))^2 )^1/2

Assumes that XL is 0.

500= (100 - XC^2)^1/2

250000 = 100 - XC^2

XC = 500,1

This is incorrect. Can someone please help me?

Where do you get that you subtract off the reactance? Think of it in terms of the sides of a triangle -- the resistance is one side and the net reactance is the other. The impedance is the length of the hypotenuse, which is the square root of the sum of the squares of the sides.

And please start using units in your work.

 

Understand, XC should be = 499.9 ohms

And for the power factor we have:

P = I^2 * R = 0.2^2 A *10 = 0.4 W
S = I^2 * Z = 0.2^2 A * (10+499.9) ohms = 20.4 VA

PF = 0.4/ (20.4) = 0.0196

 

Understand, XC should be = 499.9 ohms

And for the power factor we have:

P = I^2 * R = 0.2^2 A *10 = 0.4 W
S = I^2 * Z = 0.2^2 A * (10+499.9) ohms = 20.4 VA

PF = 0.4/ (20.4) = 0.0196

But I haven't taken the 60-cycle/sec source into account, which making this calculation incorrect.

 

Understand, XC should be = 499.9 ohms

And for the power factor we have:

P = I^2 * R = 0.2^2 A *10 = 0.4 W
S = I^2 * Z = 0.2^2 A * (10+499.9) ohms = 20.4 VA

PF = 0.4/ (20.4) = 0.0196

You are at least trying to track units. Sort of.

Power consumption:

P = I^2 * R = (0.2A)^2 *10Ω = 0.4 W

A^2 times Ω is W. You can convert them to base (or at least more basic) units and verify this. You need to get in the habit not only of writing down the units, but tracking them. Meaning that when you write the 0.4W you ask yourself if amps squared time ohms is watts and only proceed if you are sure that it does.

Now, S is apparent power (or, more accurately, complex power with apparent power being the magnitude of it).

S = I^2 * Z = (0.2A)^2 * (10+499.9) ohms = 20.4 VA <== WRONG!

The magnitude of the impedance is NOT the algebraic sum of the resistance and the reactance. This is a vector quantity. But you also know that the apparent power is simply the rms voltage multiplied by the rms current. so what does that give you.

 

But I haven't taken the 60-cycle/sec source into account, which making this calculation incorrect.

Okay, so if you know that not taking the 60-cycle/sec into account somehow makes the calculation incorrect, why didn't you take it into account?

What difference would it have made in the result?

 

Thanks for reply. I think I have figured out the solution.

a) 500 ohms

b) 0.2 ^2 A * 10 ohms = 0.4 W

c) S= Vrms * I rms = 20 VA

PF = P/S = 0.4 w / 20 VA = 0.02

d) PF gives a phase ange between voltage and current: 88.9

Xc = Z sin 88.9 = 499.9 ohms

 

You've basically got it. There are just a couple of minor points you are still messing up.

0.2 ^2 A * 10 ohms = 0.4 W

You need to square 0.2A to get 0.04 A^2 and not 0.04 A. The units are physical quantities that take part in the same operations as their coefficients. If you don't do that correctly, then they are meaningless. If you do do it correctly, you can catch the majority of your mistakes which will result in better grades now and less death and distruction later. Remember, doctors kill people one at a time, engineers do it in job lots!

Second, the phase angle is -88.9 degrees. Strictly speaking, reactance is a signed quantity that is positive for inductive reactance and negative for capacitive reactance. Not all authors are careful about that, which is a shame, but if you are only going to treat all reactance as a magnitude only, then you have to explicitly track and state whether it is inductive or capacitive at every step, which is cumbersome and error prone. Far better just to have inductive reactance be positive and capacitive reactance be negative. Then you can add reactances and let the chips fall where they will and interpret the results at any given point based on whether the reactance is positive or negative.

 

Oh, and you need to check to see if your answers actually answer the questions that were asked.

a) the impedance of the circuit,

This should consist of two parts, a magntitude and an phase angle.

b) the power consumption,

This should be in watts and is the power actually dissipated by the circuit.

c) the power factor,

This should be a number less than or equal to 1 and an indication of whether it is leading or lagging.

d) the value of capacitance

This should be in farads.