(III) A hollow cylindrical resistor with inner radius r and outer radius r2, and length &, is made of a material whose resis- tivity is p (Fig. 25-36). (a) Show that the resistance is given by R = In 2nl for current that flows radially outward. [Hint: Divide the resistor into concentric cylindrical shells and integrate. (b) Evaluate the resistance R for such a resistor made of carbon whose inner and outer radii are 1.0 mm and 1.8 mm and whose length is 2.4 cm. (Choosep = 15 x 10-0 m.) (c) What is the resistance in part (b) for current flowing parallel to the axis?
(III) A hollow cylindrical resistor with inner radius r and outer radius r2, and length &, is made of a material whose resis- tivity is p (Fig. 25-36). (a) Show that the resistance is given by R = In 2nl for current that flows radially outward. [Hint: Divide the resistor into concentric cylindrical shells and integrate. (b) Evaluate the resistance R for such a resistor made of carbon whose inner and outer radii are 1.0 mm and 1.8 mm and whose length is 2.4 cm. (Choosep = 15 x 10-0 m.) (c) What is the resistance in part (b) for current flowing parallel to the axis?
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P-1 Please help me with this problem very clearly with step by step explanation.
Take the length to be 3.0 cm (not 2.4 cm) and the resistivity to be 3.0 x 10-5 W.m.
![30. (III) A hollow cylindrical resistor with inner radius r and
outer radius r2, and length (, is made of a material whose resis-
tivity is p (Fig. 25-36). (a) Show that the resistance is given by
In
2nl
R =
for current that flows radially outward. [Hint: Divide the
resistor into concentric cylindrical shells and integrate.]
(b) Evaluate the resistance R for such a resistor made of
carbon whose inner and outer radii are 1.0 mm and 1.8 mm
and whose length is 2.4 cm. (Choose p = 15 x 100 m.)
(c) What is the resistance in
part (b) for current flowing
parallel to the axis?
FIGURE 25-36
Problem 30.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8302e9db-771b-47a3-89ce-b381b0fba447%2F59c24534-3198-4221-9f51-c1c9892f869e%2Fhgkmxe_processed.png&w=3840&q=75)
Transcribed Image Text:30. (III) A hollow cylindrical resistor with inner radius r and
outer radius r2, and length (, is made of a material whose resis-
tivity is p (Fig. 25-36). (a) Show that the resistance is given by
In
2nl
R =
for current that flows radially outward. [Hint: Divide the
resistor into concentric cylindrical shells and integrate.]
(b) Evaluate the resistance R for such a resistor made of
carbon whose inner and outer radii are 1.0 mm and 1.8 mm
and whose length is 2.4 cm. (Choose p = 15 x 100 m.)
(c) What is the resistance in
part (b) for current flowing
parallel to the axis?
FIGURE 25-36
Problem 30.
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