Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 25, Problem 49P
To determine
The expression for resistance of the wire.
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A cylindrical conductor has resistance of R0 = 950 Ω. It has length L, radius of the cross section r, and resistivity ρ.
a) If the resistivity was restored to its original value and instead the length of the conductor decreased by a factor of 2, what would the value of the new resistance be, in ohms?
b) If the resistivity and length of the conductor were at their original values and the radius of the conductor increased by a factor of 4, what would be the value of the new resistance, in ohms?
The resistivity of copper is 1.72E-8 Ω·m. We would like to use a copper wire to connect two devices that are 6.65 m apart and require the wire resistance to be no higher than 7.21E-3 Ω. What is the minimum cross section area of the copper wire that we should use (in m2)?
2.
Page
> of 3
5. Two long coaxial metal cylinders with radii a and b are separated by material of
conductivity o (see figure below). The conductivity is not uniform and changes as
= (s)0
where k is a constant. If the two cylinders are kept at a potential difference V,
find the resistance R between the cylinders.
(s)o
Hint: Since the conductivity is a function of position, the charge density in the resistive
medium is not zero and E does not go like 1/s. However, since the current I is steady, the
same current flows across each eylindrical surface. Instead of using Gauss' Law, find E
in terms of I, from Ohm's Law.
acer
F10
F11
Chapter 25 Solutions
Physics for Scientists and Engineers
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- Part (a) I measure the resistance of this wire and find it to be R = 156 Q. What is the resistivity of the material the wire is made out of? p= Problem 7: A particular wire has a length of L = 2.7 m and a circular cross-sectional area of radius r= 1.69 mm. G= sin() cos cotan() asin()) acotan() atan() cosh() tanh() I= sin()) cos() cotan() asin() sinh() atan() acotan cosh() tanh() cotanh() Degrees O Radians B Degrees O Radians Part (b) What is the conductivity of this wire, in inverse Ohms per meter? 0 tan()) π ( acos() E ^^^L sinh() cotanh() g L P Y d h m r tan() π acos() E ^^^^ π E 1 Part (c) Give an expression for the current density in the wire if an electric field E is passing through it. Write this in terms of the resistivity and the other variables in the problem. J= n R ( ^^^ sin() cos() cotan() asin() atan() acotan() cosh() + + 7 8 9 4 5 6 1 2 3 0 END NO BACKSPACE DEL CLEAR Part (d) Calculate the current in the wire, in milliamperes, if the field strength is 5.28 V/m. - END NO…arrow_forwardWire C and wire D are made from the same material of resistivity p- 2.0 x 10 am. The length and radius of wire Care Le 1.0m and re 2.00 mm, and those of wire D are Le- 0.50.m and ro-0.75 mm. The wires are joined as shown in the figure. What is the resistance R between points 1 and 2?arrow_forwardA cylindrical conductor with resistivity ρ, length L, and radius r , has resistance R0=302Ω. If the resistivity and the length of the conductor both have their original values, but instead the radius of the conductor is increased by a factor of 5, what is the new value, in ohms, of the resistance?arrow_forward
- Two copper wires (call them A and B) both have length 19.0 m but wire A has a radius 7.045 mm and wire B has a radius 2.668 mm. What is the ratio of the resistances of the two wires? The resistivity of copper is 1.68x10-8 Ω/m. Report your answer to three decimal places.arrow_forwardA cylindrical conductor has resistance of R0 = 140 Ω. It has length L, radius of the cross section r, and resistivity ρ. Part (a) Express the resistance in terms of L, r, ρ. Part (b) If the resistivity increases by a factor of 5, what would the value of the new resistance be, in ohms? Part (c) If the resistivity was restored to its original value and instead the length of the conductor decreased by a factor of 5, what would the value of the new resistance be, in ohms? Part (d) If the resistivity and length of the conductor were at their original values and the radius of the conductor increased by a factor of 4, what would be the value of the new resistance, in ohms?arrow_forwardThe radius r of a wire grows linearly with its length I according to r(2) = a+x, where z is the distance from the thinner end of the wire with radius a. Express the resistance as a function of the resistivity of the material p, the length of the wire I and the radii a and b. View Available Hint(s ?arrow_forward
- Two identical resistors of R0 = 98 Ω are connected head-to-tail. Express the resistance R0 of one of the resistors in terms of the resistivity ρ, length L, and the cross section area A. Calculate the total resistance R of the two resistors in ohms.arrow_forwardA copper (resistivity = 1.72 EXP-8 Ω.m) conductor with a square cross section, 1.0 mm on a side is 100 m long and is initially 20oC. 1. If the temperature coefficient (a) of copper is 0.00393 per degree Celsius, what is the change in resistance of the copper conductor if the temperature is increased to 100 degrees Celsius? 2. What is the resistance of this conductor?arrow_forwardThe resistivity of silver ρ = 1.61 x 10-8 Ω.m. If you have a length of silver wire that is 3.15 m in length, and that has a cross-sectional diameter of 482 μm, what is the resistance of that wire (in Ω, or Ohms)?arrow_forward
- An iron wire has a diameter 6.05 mm and resistivity 9.71x 10-8 Qm. What will be the length of this wire to make a resistance of 400. What will be the new resistance, if the radius is doubled? (a) Length of the wire (in m) = (b) Resistance of the wire (in = Finish attempt .. NG 4) GO f2 f3 O f4 O f6 D f7 ) f8 f9 * f10 3 $ &y 4 7 8. R 28 Y Se D[ F 1 GY H i K -u ) 43 ) # 3arrow_forwardAn iron wire has a diameter 7.25 mm and resistivity 9.71x 10- Qm. What will be the length of this wire to make a resistance of 100. What will be the new resistance, if the radius is doubled? (a) Length of the wire (in m) = (b) Resistance of the wire (in )2 = Fe to search DELLarrow_forwardTwo identical resistors of R0=32 omega are connected head to tail. Part (a) Express the resistance R0 of one of the resistors in terms of the resistivity, length L, and the cross section area A. Part (b) calculate the total resistance R of the two resistors in ohms.arrow_forward
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