The potential difference between points in a wire 10m apart

The potential difference between points in a wire 10m apart is 12 v if the wire has a radius of 2.0 times 10^-3 m. 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 12V battery for 60 s? what is the mass of the wire how much does the temperature of the wire increase A carbon resistor is to be used as a thermometer. On a winter day when the temperature is freezing, its distance is 237.5 Q what is the temperature on a hot summer day when resistance is 233.9 ohm? What is the current flows through the resistor in the winter if the ohmmeter uses a 1.5 V battery?

Solution

a)

Electric field

E=V/L =12/10 =1.2 V/m

b)

Resistivity of wire

p =E/J =1.2/4*10⁷

p=3*10^-8 ohm-m

c)

Area

A=pi*r² =pi*(2*10^-5)²=1.2566*10^-9 m²

Resistance of the wire

R=pL/A =(3*10^-8)*10/(1.2566*10^-9)

R=238.7 ohms

d)

Current in the wire

I=V/R =12/238.7

I=0.05027 A

e)

Power dissipated in the resistor is

P=I²R=0.05027²*238.7

P=0.603 Watts