The potential difference between points in a wire 10 m apart is 12 V when the cu

Question

The potential difference between points in a wire 10 m apart is 12 V when the current density is 4 Times 10^7 A/m^2. If the wire has a radius of 2.0 Times 10^-3 m, find the electric field in the wire, the resistivity of the material in the wire, the resistance of the wire, the current in the wire, and the power dissipated in the wire. What is the resistance of a copper wire of radius 1.0 Times 10^-4 m and length 2.0 Times 10^3 m? How much energy is converted into heat when this wire is connected to a 12 V battery for 60 s? What is the mass of the wire How much does the temperature of the wire increase (assuming no heat loss to the surroundings)? How much does the resistance of the wire increase due to this heat? A carbon resistor is to be used as a thermometer. On a winter day when the temperature is freezing, its resistance is 237.5 Ohm. What is the temperature on a hot summer day when the resistance is 233.9 OhmQ? What current flows through the resistor in the winter if the ohmmeter uses a 1.5 V battery? How much power does resistor dissipate in the winter if it takes 5 seconds to measure its resistance?

Explanation / Answer

4.

a)

Resistance = p * L/area

Resistance = 1.72 *10^-8 * 2*10^3/(pi *(1 *10^-4)^2)

Resistance = 1095 Ohm

the resistance of wire is 1095 Ohm

b)

energy dissipated in 60 s = V^2 * t/R

energy dissipated in 60 s = 12^2 * 60/1095

energy dissipated in 60 s = 7.89 J

c)

mass of wire = Volume * density of wire

mass of wire = pi * r^2 * L * density

mass of wire = pi * (1 *10^-4)^2 * 2 *10^3 * 8900 Kg

mass of wire = 0.559 Kg

d)

as energy = mass * S * delta T

7.89 = 0.559 * 390 * delta T

delta T = 0.036 degree C

the increase in tempeature is 0.036 degree C

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