Question

While taking photographs in Death Valley on a day when the temperature is 55.0°C, Bill Hiker finds that a certain voltage applied to a platinum wire produces a current of 1.000 A. Bill then travels to Antarctica and applies the same voltage to the same wire. What current does he register there if the temperature is −88.0°C? Assume no change occurs in the wire's shape and size.

Answer 1

Temperature coefficient of resistance of copper, α = 0.004041 per K

Temperature at Death valley, t1 = 55 deg c

Temperature at Antarctica, t2 = - 88 deg c

Current at Death valley, i1 = 1.000 A

Current at Antarctica, i2 = ?

Let

Voltage = V

Solution:

Variation of resistance with temperature:

             R2 = R1 [ 1 + α ( t2- t1 ) ]

             R2 / R1 = 1 + (0.004041) ( - 88 - 55 )

                          = 1 - 0.57

                          = 0.42

According to Ohm's law,

           V = i R

So, i2 / i1 = R1 / R2   [ since V = constant ]

      i2 / i1 = 1 / 0.42

            i2 = 1 * ( 1 / 0.422 )

                = 2.36 A

Ans:

Current at Antarctica, i2 = 2.36 A