Tutorial Exercise An air-filled spherical capacitor is constructed with an inner-shell radius of 6.95 cm and an outer-shell radius of 14.5 cm. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a 4.00-μC charge on the capacitor? Part 1 of 4 - Conceptualize Since the separation between the inner and outer shells is much larger than a typical electronic capacitor with separation on the order of 0.1 mm and capacitance in the microfarad range, we expect the capacitance of this spherical configuration to be on the order of picofarads. The potential difference should be sufficiently low to avoid sparking through the air that separates the shells. Part 2 of 4 - Categorize We will calculate the capacitance from the equation for a spherical shell capacitor. We will then calculate the voltage found from Q = CAV. Part 3 of 4 - Analyze (a) For a spherical capacitor with inner radius a and outer radius b, we have the following for the capacitance. ab C = k₂(b-a) 0.0695 0.0695 m 0.145 0.145 m . (8.99 x 109 N m²/c²) 0.145 0.145 m 0.0695 1.484 1.48 x 10 11 F = 14.84 14.8 PF Part 4 of 4 - Analyze (b) The change in voltage across a capacitor of charge Q is given by AV = 5 × 0.0695 m Your response differs from the correct answer by more than 10%. Double check your calculations. x 1.484 × 10-11 F) Your response differs from the correct answer by more than 10%. Double check your calculations. KV. 10-6 c) = = 337
Tutorial Exercise An air-filled spherical capacitor is constructed with an inner-shell radius of 6.95 cm and an outer-shell radius of 14.5 cm. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a 4.00-μC charge on the capacitor? Part 1 of 4 - Conceptualize Since the separation between the inner and outer shells is much larger than a typical electronic capacitor with separation on the order of 0.1 mm and capacitance in the microfarad range, we expect the capacitance of this spherical configuration to be on the order of picofarads. The potential difference should be sufficiently low to avoid sparking through the air that separates the shells. Part 2 of 4 - Categorize We will calculate the capacitance from the equation for a spherical shell capacitor. We will then calculate the voltage found from Q = CAV. Part 3 of 4 - Analyze (a) For a spherical capacitor with inner radius a and outer radius b, we have the following for the capacitance. ab C = k₂(b-a) 0.0695 0.0695 m 0.145 0.145 m . (8.99 x 109 N m²/c²) 0.145 0.145 m 0.0695 1.484 1.48 x 10 11 F = 14.84 14.8 PF Part 4 of 4 - Analyze (b) The change in voltage across a capacitor of charge Q is given by AV = 5 × 0.0695 m Your response differs from the correct answer by more than 10%. Double check your calculations. x 1.484 × 10-11 F) Your response differs from the correct answer by more than 10%. Double check your calculations. KV. 10-6 c) = = 337
Chapter8: Capacitance
Section: Chapter Questions
Problem 84CP: A capacitor has parallel plates of area 12 cm2 separated by 2.0 mm. The space between the plates is...
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Transcribed Image Text:Tutorial Exercise
An air-filled spherical capacitor is constructed with an inner-shell radius of 6.95 cm and an outer-shell radius of 14.5 cm.
(a) Calculate the capacitance of the device.
(b) What potential difference between the spheres results in a 4.00-μC charge on the capacitor?
Part 1 of 4 - Conceptualize
Since the separation between the inner and outer shells is much larger than a typical electronic capacitor with separation on the order of 0.1 mm and capacitance in the microfarad range, we expect the
capacitance of this spherical configuration to be on the order of picofarads. The potential difference should be sufficiently low to avoid sparking through the air that separates the shells.
Part 2 of 4 - Categorize
We will calculate the capacitance from the equation for a spherical shell capacitor. We will then calculate the voltage found from Q = CAV.
Transcribed Image Text:Part 3 of 4 - Analyze
(a) For a spherical capacitor with inner radius a and outer radius b, we have the following for the capacitance.
ab
C =
k₂(b-a)
0.0695
0.0695 m 0.145
0.145 m
.
(8.99 x 109 N m²/c²) 0.145
0.145 m 0.0695
1.484
1.48 x 10 11 F = 14.84
14.8 PF
Part 4 of 4 - Analyze
(b) The change in voltage across a capacitor of charge Q is given by
AV =
5
×
0.0695 m
Your response differs from the correct answer by more than 10%. Double check your calculations. x
1.484
× 10-11
F)
Your response differs from the correct answer by more than 10%. Double check your calculations. KV.
10-6 c) =
= 337
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