Chapter 4.6, Problem 2E

Interpretation Introduction

Interpretation:

To check the qualitative solution by integrating equation $\text{4}\text{.6}\text{.7}$ and to plot the graph of ${\text{I}}_{\text{c}}\text{sin}\varphi \text{(t) Vs}\text{. V(t)}$

Concept Introduction:

The Josephson junction is a superconducting device that generates high frequency voltage oscillations. The junction consists of two closely spaced conductors that are separated by the weak connection. The equation for the Josephson’s circuit for the over damped condition is given as:

${\varphi }^{\prime }=\frac{\text{I}}{{\text{I}}_{\text{c}}}-\sin \varphi$, while $I_c$ is the critical current

The Josephson’s voltage phase relation is given as

$\text{V}=\frac{\hslash }{\text{2e}}\dot{\varphi }$, while $\hslash$ is the planks constant