Semiconductor resistor in series with a capacitor -- Energy gap

[Granger]

Homework Statement

Consider a circuit that consists on a resistor of an intrinsic semiconductor R and a capacitor C in series. The voltage between the terminals of the circuit is U, which is an alternated sinusoidal voltage.
U1, which is the voltage in the capacitor as a phase difference of 30 degrees from the voltage U for a temperature of 300K and a phase difference of 9 degrees at 330 K
What is the energy gap in the

Homework Equations

I = jwC Uc

The Attempt at a Solution

I have no idea where to start.
I know that I have to relate my voltages but I have no idea how, since they just say they have a ohase difference.
I know that the fraction between the phasors of U and U1 must then be $$e^{j\pi/6}$$. But how do I relate this to the resistance?
This j however confuses me...

Then after I get my resistances I know how to proceed

By applying:
$$R/R'=e^{\frac{W_G(T'-T)}{2KTT'}}$$

And solving this equation I get W_G.

So yeah basically my problem is how to work the circuit to find the resistance.

Can someone give me a little help?

 

[KataKoniK]

Hi there,

To find the resistance in this circuit, you will need to use Ohm's Law, which states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. In this case, the voltage across the resistor is U, and the current through the resistor is I. So we can write:

$$I=\frac{U}{R}$$

We can also use the equation given in the problem to relate the voltage across the capacitor, Uc, to the voltage across the resistor, U:

$$Uc=Ue^{j\pi/6}$$

Using this equation, we can substitute for Uc in the first equation:

$$I=\frac{Ue^{j\pi/6}}{R}$$

Now, we can use the given equation for the current through the capacitor, I=jwCUc, to solve for R:

$$I=\frac{jwCUc}{R}$$

Substituting for Uc, we get:

$$I=\frac{jwCUe^{j\pi/6}}{R}$$

Finally, we can solve for R:

$$R=\frac{jwCUe^{j\pi/6}}{I}$$

This should give you the resistance in terms of the other variables. Let me know if you have any other questions.