What is the solution to the non-linear device problem?

[jegues]

Homework Statement

See figure

Homework Equations

The Attempt at a Solution

Again, see figure I tried something and it looked promising but the answer doesn't work out.

Any ideas?

 

[vela]

Could you explain your reasoning to get the equation

$$\frac{1+v_Q/i_Q}{2+v_Q/i_Q} = 10$$

I don't see how you're applying Kirchoff's voltage law to get that.

 

[wwshr87]

You know the 1 ohm resistor is in parallel with the 10V source, therefore the voltage across it is 10V. Now we can subtract from the 10V the drop across the other 1 ohm resistor which is 1*Iq, and subtract Vq. 10 - 1*Iq - Vq=0, we can plug in for Iq which is Vq^2+2*Vq. Solve for Vq, you'll obtain a positive and negative value but only the positive makes sense because of our polarity.

 

[Zryn]

When you combine the circuit resistances, first by adding the two in series, and then by calculating the two in parallel, you get a value of resistance (keep in mind SI units).

In your equations you say this resistance is equal to 10 volts by KVL.

$$\frac{1+v_Q/i_Q}{2+v_Q/i_Q} = 10$$

Resistance does not equal voltage.

 

[jegues]

Thanks for the responses. I must have been out of it at the time putting resistance equal to voltage lol.

I understand now.

$$V_{q} = 2V$$