A spherical shell with inner radius r, and outer radius r, isformed from a material of resistivity p. It carries currentradially, with uniform density in all directions. Show thatits resistance is1R=4T \'a(G-)#-

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University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

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Chapter9: Current And Resistance

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Problem 89CP: Consider a resistor made from a hollow cylinder of carbon as shown below. The inner radius of the...

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Consider a resistor made from a hollow cylinder of carbon as shown below. The inner radius of the cylinder is Ri= 0.20 mm and the outer radius is R0 = 0.30 mm. The length of the resistor is L = 0.90 mm. The resistivity of the carbon is =3.5105 m. (a) Prove that theresistance perpendicular from the axis is R=2L1n(R0Ri) . (b) What is the resistance?
Consider a power plant is located 60 km away from a residential area uses Q-gauge (A=42.40mm2) wire ofcopper to transmit power at a current of I = 100.00 A.How much more power is dissipated in the copper wires than it would be in superconducting wires?
A 10-gauge copper wire has a cross-sectional area A=5.26mm2 and carries a current of I=5.00A . The adensity of copper is =89.50g/cm2 . One mole ofcopper atoms (6.021023atoms) has a mass ofapproximately 63.50 g. What is the magnitude of the drift velocity of the elections, assuming that each copper atom contributes one free electron to the current?
A piece of material with a square cross-section measuring 1 mm on each side has a length of 1 m. What is the resistance of this material if it were made of aluminium? Fused quartz? Finally, calculate the current through each piece of material if a potential difference of 1 volt is applied over its length.
A 500-W heating coil designed to operate from 110 V ismade of Nichrome wire 0.500 mm in diameter.(a) Assuming the resistivity of the Nichrome remains constantat its 20.0°C value, find the length of wire used.(b) What If? Now consider the variation of resistivity withtemperature. What power is delivered to the coil of part(a) when it is warmed to 1 200°C?
Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at 20.0ºC ?
A potential difference of 12 V is found to produce a currentof 0.40 A in a 3.2 - m length of wire with a uniform radius of0.40 cm. What is (a) the resistance of the wire? (b) The resistivityof the wire?
Consider a resistor of resistivity 3.96 × 10-8 Ω • m. If an electric field of 12 V/m is applied across the resistor and the electron volume concetration in the conductor is 5.16 × 1028 per m3, determine the drift velocity, in mm/s, of the free electron constituting the current.
Two long coaxial metal cylinders (radii a and b) with a length L, are separated bymaterial of uniform conductivity σ. If they are maintained at a potential difference V, findthe followings:1) current flow (I) and resistance (R)2) If the material is not uniform, let σ=k/s (k is a constant), find I and R.
A 500-W heating coil designed to operate from 110 V is made of Nichrome wire 0.500 mm in diameter. (a) Assuming the resistivity of the Nichrome remains constant at its 20.0°C value, find the length of wire used. (b) What If? Now consider the variation of resistivity with temperature. What power is delivered to the coil of part (a) when it is warmed to 1 200°C?
Consider a resistor of resistivity 3.89 × 10-5 Ω • m, length 15.21 m, and unknown cross-sectional area. What potential difference, in millivolts, should be applied across the said resistor so the current density in it is 36.69 A/m2?
A metal object having a length (10m), cross section area (0.5 mm2), and resistance (0.52) is connected to a potential difference source of 5V at room temperature. If the density of free electrons equals (8×1025 electron/m³), Calculate the thermal velocity.

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A spherical shell with inner radius r, and outer radius r, is formed from a material of resistivity p. It carries current radially, with uniform density in all directions. Show that its resistance is 1 R= 4T \'a (G-)#-