Chapter 4.6, Problem 6E

Interpretation Introduction

Interpretation:

To draw the circuit where $\text{N}$ junction is in series and where the load is a resistor $\text{R}$ in series with a capacitor $\text{C}$ and inductor $\text{L}$. Find the differential equation for ${\varphi }_k$ and $\text{Q}$, where $\text{Q}$ is the charge on the load capacitor.

Concept Introduction:

Superconducting devices also known asJosephson Junctions. They are capable of generating high voltage frequency oscillations.

The Josephson current phase relation is ${\text{I = I}}_{\text{c}}\text{sin}\varphi$, and voltage phase relation is $\text{V=}\frac{\hslash }{\text{2e}}\dot{\varphi }$.

Using Kirchhoff’s current law, we can find the differential equation for ${\varphi }_k$, and using Kirchhoff’s voltage law, we can find the differential equation for $\text{Q}$.