# A Circuit with Nonlinear Element—finding element's current & voltage

• JessicaHelena
In summary, the conversation discusses the approach to solving a circuit problem and suggests using KCL and simplifying the circuit using Thevenin equivalent. The concept of load lines and their usefulness in dealing with non-linear characteristics is also mentioned. The conversation ends with a suggestion to try different values of ix and rx to find the desired operating point.
JessicaHelena
Homework Statement
Lem bought a mystery apparatus at an electrical flea market. One element in the apparatus was unmarked and not obviously identified, but when he measured its behavior in a curve tracer he found that it was a nonlinear resistor with the characteristic shown in Figure 1.

In the circuit that Lem found this the strange element, it was connected to a power supply of 𝑉𝑠=5.0 V with a series resistance of 𝑅𝑠=4700.0Ω and it was shunted with a parallel resistance of 𝑅𝑝=8200.0Ω . (Refer to Figure 2.)

1. What is the current (in Amperes) through the strange object when it is in operation in the circuit?

2. What is the voltage (in Volts) across the strange object when it is in operation in the circuit?
Relevant Equations
KVL, KCL
I don't really understand or see the correct way to approach this.

Letting the current in question be ##i_x## (as shown in Fig. 1), and the unknown (changing) resistance be $R_x$, I can write:
##-V_s + R_s i_s + i_x R_x = 0##, and ##R_p i_p = i_x R_x##. Hence we can also write ##-V_s + R_s i_s + R_p i_p = 0##.

From KCL I have that ##i_s = i_p + i_x##.

Also, ##i_s = V_s/(R_s + \frac{1}{\frac{1}{R_x} + \frac{1}{R_p}}).##

Then I have an equation that looks like ##V_s + R_pi_x = (R_s + R_p) \cdot i_s##, which doesn't seem to simplify at all...

#### Attachments

• Figure 1.png
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• Figure 2.png
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JessicaHelena said:
way to approach this
You can ask yourself 'what is the maximum ##i_x## and what is the maximum ##V_x## ?

Note that the suggestive form ##R_x## is only applicable in a certain range of ##V_x## and ##i_x##, you want to check what range applies !

I might suggest that you first simplify the circuit, combining the known conventional components into a Thevenin equivalent.

Question: Have you covered the concept of load lines in your course? These are very handy when a device has non-linear characteristics. Transistors are a good example of this where you can draw a load line over the characteristic curves to find the operating point.

BvU
Up to ix=1 mA Rx=1/0.001=1000 ohm

If ix>1mA[0.001 A] then (vx-1)/(ix-1/1000)=(3-1)/[(2-1)/1000]- ix in A.

Take ix=0.001 A then Rx=1000 ohm and recalculate ix.Then reuse the resulted ix. If you get the same ix eventually that's what you're looking for.

## 1. What is a nonlinear element in a circuit?

A nonlinear element in a circuit is an element that does not follow Ohm's law, which states that the current through a conductor is directly proportional to the voltage applied across it. Nonlinear elements have a more complex relationship between current and voltage, often exhibiting behaviors such as hysteresis, saturation, and non-constant resistance.

## 2. Why is it important to find the current and voltage of a nonlinear element in a circuit?

It is important to find the current and voltage of a nonlinear element in a circuit because it allows us to understand and analyze the behavior of the circuit. By knowing the current and voltage of the nonlinear element, we can determine how it affects the overall circuit and make necessary adjustments for optimal performance.

## 3. How do you find the current and voltage of a nonlinear element in a circuit?

The current and voltage of a nonlinear element can be found using techniques such as Kirchhoff's laws, Thevenin's theorem, and nodal analysis. These methods involve applying circuit analysis equations and solving for the unknown variables.

## 4. What challenges may arise when finding the current and voltage of a nonlinear element in a circuit?

One challenge that may arise is the complexity of the equations involved in solving for the current and voltage of a nonlinear element. In some cases, it may also be difficult to accurately model the nonlinear behavior of the element, leading to errors in the calculations.

## 5. How can the current and voltage of a nonlinear element be used in circuit design?

The current and voltage of a nonlinear element can be used in circuit design to optimize the performance and efficiency of the circuit. By understanding how the element behaves, designers can select components and make adjustments to achieve desired outcomes and avoid potential issues, such as overheating or excessive power consumption.

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