**For this problem, graphical answers should be drawn on the answer sheets graphs provided. Supporting work is to be written on blank answer sheets. Incorrect graphs without supporting work will receive no partial credit. **

The current I as a function of voltage V for a certain electrical device is

where q is the magnitude of the charge on an electron, k_{B} is Boltzmann’s constant, and T is the absolute temperature. I_{0} and V_{0} are non-zero positive constants. Throughout this problem assume low temperature values k_{B} T \ll q V_{0}.

a. On the answer sheets, sketch a graph of the current versus voltage for low temperature values k_{B} T \ll q V_{0}, clearly indicating any asymptotic behavior.

Shown is a schematic for the device. Positive voltage means that the electric potential of the left hand side of the device is higher than the right hand side. For this device, I_{0}=25 \mu \mathrm{A} and V_{0}=1.0 \mathrm{~V}.

Below is a circuit made up of these elements. The voltage supplied the circuit is sinusoidal, V_{A B}=V_{A}-V_{B}=V_{s} \sin \omega t, and is also shown on answer sheets. The resistance is R=5.0 \Omega and V_{s}=5.0 \mathrm{~V}.

b. Sketch the potential difference V_{C D}=V_{C}-V_{D} as a function of time on the answer sheet. For your convenience, V_{A B} is shown in light gray. Assume that V_{A B} has been running for a long time.

A capacitor is connected to the circuit as shown below. The capacitance is C=50 \mathrm{mF}.

c. Sketch the new potential difference V_{C D}=V_{C}-V_{D} as a function of time on the answer sheet. For your convenience, V_{A B} is shown in light gray. Assume that V_{A B} has been running for a long time.

**Following are the answer sheets for some of the graphical portions of the question. **

a. Sketch a graph of the current versus voltage for low temperature values k_{B }T≪ qV_{0}, clearly indicating any asymptotic behavior.

b. Sketch the potential difference V_{C D}=V_{C}-V_{D} as a function of time. For your convenience,V_{A B} is shown in light gray. Assume that V_{A B} has been running for a long time. There is no capacitor in this circuit!

c. Sketch the potential difference V_{C D}=V_{C}-V_{D} as a function of time. For your convenience, V_{A B} is shown in light gray. Assume that V_{A B} has been running for a long time. There is a capacitor in this circuit!