Question 1 a) In a closed circuit, an electric current of intensity i goes through a resistor of resistance R. The electric potential at the edges of R is measured to be V. If now we write would this generally be the definition of the resistance quantity R, or the expression of Ohm's Law? Explain. b) We define the resistivity (via the familiar notation) as E P= Thus show that the resistance R can be written as, R = p- A here L is the length of the resistor, and A is the cross-sectional area of it.

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Question 1
a) In a closed circuit, an electric current of intensity i goes through a resistor of
resistance R. The electric potential at the edges of R is measured to be V. If
now we write
would this generally be the definition of the resistance quantity R, or the
expression of Ohm's Law? Explain.
b) We define the resistivity (via the familiar notation) as
E
p=
Thus show that the resistance R can be written as,
R = p-
A
here L is the length of the resistor, and A is the cross-sectional area of it.
Transcribed Image Text:Question 1 a) In a closed circuit, an electric current of intensity i goes through a resistor of resistance R. The electric potential at the edges of R is measured to be V. If now we write would this generally be the definition of the resistance quantity R, or the expression of Ohm's Law? Explain. b) We define the resistivity (via the familiar notation) as E p= Thus show that the resistance R can be written as, R = p- A here L is the length of the resistor, and A is the cross-sectional area of it.
c) Let J the current density (i/A). Express J in terms of the electron density n
(electrons/m?), the electron drift velocity va, and the electron charge e.
d) Show that the resistivity can be expressed (via the familiar notation) as,
m
ne't
here m is the electron mass; t is the period of time that elapses between two
subsequent collisions, the electron undergoes with copper nuclei throughout
its chaotic motion in the body of copper (supposing that the current carrying
cable is made of copper). Hint: Write F=eE, i.e. the electric force reigning on
the electron. Write also the acceleration a=F/m, an electron is subject to,
based on the Newton's law of motion.
Transcribed Image Text:c) Let J the current density (i/A). Express J in terms of the electron density n (electrons/m?), the electron drift velocity va, and the electron charge e. d) Show that the resistivity can be expressed (via the familiar notation) as, m ne't here m is the electron mass; t is the period of time that elapses between two subsequent collisions, the electron undergoes with copper nuclei throughout its chaotic motion in the body of copper (supposing that the current carrying cable is made of copper). Hint: Write F=eE, i.e. the electric force reigning on the electron. Write also the acceleration a=F/m, an electron is subject to, based on the Newton's law of motion.
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