What is the unknown circuit element in RLC circuit given plot of V, I?

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    Rlc circuit
  • #1
zenterix
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Homework Statement
An AC source is connected to a single unknown circuit element as shown in the second picture below.

The driving frequency is ##\omega=100\text{rad/s}##.

The voltage and current are as in the plot in the third picture below.
Relevant Equations
Which of the following statements could be true
1714427276072.png


Here is the circuit

1714427309322.png


and here is the plot of current and voltage

1714427330490.png


we don't know which is which initially.

Just by looking at this plot, I conclude that the element cannot be a resistor because if it were then the phase would need to be zero.

Next, suppose the element is an inductor. Then

$$I_{L0}=\frac{V_{L0}}{\omega L}$$

where ##I_{L0}## and ##V_{L0}## are amplitudes of current and voltage for such a circuit.

Now, but visual inspection of the plot we see that we can have two cases.

Suppose the dashed graph is the current and the solid graph is the voltage. Then

$$\mathrm{200mA=\frac{10V}{100rad/s\cdot L}}$$

$$\implies L=\frac{1}{2}\text{H}$$

Next suppose that the dashed graph is the voltage and the solid graph is the current. Then

$$\mathrm{100mA=\frac{20V}{100rad/s\cdot L}}$$

$$\implies L=2\text{H}$$

Next, suppose the element is a capacitor. By analogous reasoning, but now using the equation

$$I_{C0}=\omega C V_{CO}$$

we reach two cases.

If the dashed line is current then we find that

$$\mathrm{200mA=100rad/s \cdot C\cdot 10V}$$

$$\implies C=\frac{0.2}{1000}=0.2\text{mF}$$

If the dashed line is voltage then

$$\mathrm{100mA=100rad/s\cdot C\cdot 20V}$$

$$\implies C=\frac{0.1}{2000}\text{F}=50\mathrm{\mu F}$$

If this is all correct I have shown that the four options selected in the first picture above are correct and that the two unselected options are incorrect. If this is so, the grading system is incorrect.

On the other hand, I guess it is more probable that I am making some mistake.
 
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  • #2
You have to figure out which curve leads the other. Read about phases and ELI the ICE man here and try again.
 
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  • #3
zenterix said:
On the other hand, I guess it is more probable that I am making some mistake.
Yes you are - you are ignoring the information about the phase difference between voltage and current shown in the graph.
 
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  • #4
Okay, that is true. The dashed line lags the solid line.

If the dashed line is current, then this is like a circuit with an inductor.

If the solid line is current, on the other hand, then this is like a circuit with a capacitor.

And indeed the grading system shows this to be correct.
 
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  • #5
zenterix said:
Okay, that is true. The dashed line lags the solid line.

If the dashed line is current, then this is like a circuit with an inductor.

If the solid line is current, on the other hand, then this is like a circuit with a capacitor.

And indeed the grading system shows this to be correct.
I agree.
Without additional information, such as curve color or line style being defined as Voltage or Current (which they are not in the problem statement), both answers would be correct.
 

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