Circuit Analysis Question

[Moneer81]

hey guys,

I have a question about this circuit that I am trying to analyze and compare my theoretical and experimental results for. So basically I have this simple circuit: an AC voltage source, a 1k resistor, 1mH inductor, and 0.1uF capacitor, all in series. We apply a 1V ground-to-peak sine wave at 1kHz. We need to find the amplitude and phase across each element.

Couple questions:
1. First, does 1V ground-to-peak mean a sine wave with amplitude 2V peak-to-peak or does it mean a 1V peak-to-peak that is always positive (i.e. the minimum is above the x-axis)?

I will try to analyze the circuit and hope you can tell me if I messed up or not:
the frequency of the circuit is 1000Hz so w = 2000pi rad/s
impedances: Z across resistor = 1000ohm
Z across inductor = jwL=(j)(2000pi)(0.001) = j2pi
Z across capacitor = 1/jwC = 1 / (j)(2000pi)(0.0000001)=-j1591

so using simple voltage division, voltage across R:
Vr = Vin(1000/1000+j2pi-j1591)= 0.53 angle 57.7
Vc = Vin(-j1591/1000+j2pi-j1591) = 0.85 angle -32.2
VL = Vin(j2pi/1000+j2pi-j1591) = 3.3E-3 angle 147.7

2. Does this seem right?

Next, we were asked to use the oscilloscope to measure the phase shift for each one of those elements with respect to the input voltage. We did that by measuring the delta t (the time delay) between two peaks: the first peak being Vin and the second one belonging to the voltage across the element. For the resistor, the two peaks were lined up (no phase shifts across a resistor) but 3. how come we see an angle of 57.7 in the above theoretical calculuation?

4. What does phase shift mean in this case anyway? the phase shift we've looked at before was the phase shift between voltage and current, which is usually 90 degrees across a capacitor and -90 across an inductor (other way around?) but I am not sure of the meaning of phase shift between the input voltage and another voltage. Isn't suposed to closer to 90 and -90 for capacitors and inductors? and why there is a phase shift across the resistor?

any help would be appreciated...thanks

 

[ericgibbs]

hey guys,

I have a question about this circuit that I am trying to analyze and compare my theoretical and experimental results for. So basically I have this simple circuit: an AC voltage source, a 1k resistor, 1mH inductor, and 0.1uF capacitor, all in series. We apply a 1V ground-to-peak sine wave at 1kHz. We need to find the amplitude and phase across each element.

Couple questions:
1. First, does 1V ground-to-peak mean a sine wave with amplitude 2V peak-to-peak or does it mean a 1V peak-to-peak that is always positive (i.e. the minimum is above the x-axis)?
I would read this as a sinewave that swings thru zero [gnd] to 1Vpk either side of 0v.


4. What does phase shift mean in this case anyway? the phase shift we've looked at before was the phase shift between voltage and current, which is usually 90 degrees across a capacitor and -90 across an inductor (other way around?) but I am not sure of the meaning of phase shift between the input voltage and another voltage.
The phase shift in this example is the shift in phase of the measured waveforn relative to input waveform, which is your reference.

Isn't suposed to closer to 90 and -90 for capacitors and inductors?
Are you 'sure' that the phase shift is always closer to +/-90deg for reactive components??

and why there is a phase shift across the resistor?
You have to consider the current flowing in the composite series circuit as a complete circuit,
the reactive components effect the current in the series network,
so what effect would you expect in the resistor current, [which gives you the scope voltage???]

Hi,
I havn't checked your calculations, thats just formula's and a calculator.

I would suggest you consider the 'current' flowing in the network rather than the voltages when visualising the waveforms.
Hope this helps.

 

[ljcox]

hey guys,

I have a question about this circuit that I am trying to analyze and compare my theoretical and experimental results for. So basically I have this simple circuit: an AC voltage source, a 1k resistor, 1mH inductor, and 0.1uF capacitor, all in series. We apply a 1V ground-to-peak sine wave at 1kHz. We need to find the amplitude and phase across each element.

Couple questions:
1. First, does 1V ground-to-peak mean a sine wave with amplitude 2V peak-to-peak or does it mean a 1V peak-to-peak that is always positive (i.e. the minimum is above the x-axis)? Gnd to peak means just that. So it is 2V p-p.

I will try to analyze the circuit and hope you can tell me if I messed up or not:
the frequency of the circuit is 1000Hz so w = 2000pi rad/s
impedances: Z across resistor = 1000ohm
Z across inductor = jwL=(j)(2000pi)(0.001) = j2pi = j6.28 approx
Z across capacitor = 1/jwC = 1 / (j)(2000pi)(0.0000001)=-j1591

The "Z across" does not make sense. The resistance is 1000 Ohm, the reactance of the L is j2pi the reactance of the C is -j1591 assuming that your arithmetic is correct.

so using simple voltage division, voltage across R:
Vr = Vin(1000/{1000+j2pi-j1591})= 0.53 angle 57.7
Vc = Vin(-j1591/{1000+j2pi-j1591}) = 0.85 angle -32.2
VL = Vin(j2pi/{1000+j2pi-j1591}) = 3.3E-3 angle 147.7

2. Does this seem right? I have not checked the maths but it looks like you're using the voltage divider formula. If so, you need the brackets that I added.

Next, we were asked to use the oscilloscope to measure the phase shift for each one of those elements with respect to the input voltage. We did that by measuring the delta t (the time delay) between two peaks: the first peak being Vin and the second one belonging to the voltage across the element. For the resistor, the two peaks were lined up (no phase shifts across a resistor) but 3. how come we see an angle of 57.7 in the above theoretical calculuation? It is more accurate to measure the time between zero crossings. The phase angle of the voltage across the resistor is because of the current phase angle.

4. What does phase shift mean in this case anyway? the phase shift we've looked at before was the phase shift between voltage and current, which is usually 90 degrees across a capacitor and -90 across an inductor (other way around?) but I am not sure of the meaning of phase shift between the input voltage and another voltage. Isn't suposed to closer to 90 and -90 for capacitors and inductors? and why there is a phase shift across the resistor?
If there was only a capacitor or inductor in the circuit, the phase shift betweeen voltage and current would be 90 deg. But in this case, you have resistance also.
any help would be appreciated...thanks

In the case of a series circuit, the common parameter is the current since it flows through all components.

In the case of a parallel circuit, the common parameter is the voltage since it across all components.

The way I would do it is as follows:-

1. find the current from I= V/Z
where Z = r + j(Xl - Xc) = 1000+j2pi-j1591 = 1000 +j6.28 - j1591 = 1000 -j1585 approx

2. the voltage across the r will be I * r.

3. the voltage across the L will be I * Xl.

4. the voltage across the C will be I * Xc.

 

[Moneer81]

Thank you very much for the help

 

[ljcox]

Thank you very much for the help

You're welcome.

One point that I forgot yesterday. Did you draw a phasor diagram?

I think it would help you to visualise the situation.