Solution Found!
Answer: A 1.50-m cylindrical rod of diameter 0.500 cm is
Chapter 25, Problem 11E(choose chapter or problem)
Problem 11E
A 1.50-m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0°C) the ammeter reads 18.5 A, while at 92.0°C it reads 17.2 A. You can ignore any thermal expansion of the rod. Find (a) the resistivity at 20.0o C and (b) the temperature coefficient of resistivity at 20o C for the material of the rod.
Questions & Answers
QUESTION:
Problem 11E
A 1.50-m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0°C) the ammeter reads 18.5 A, while at 92.0°C it reads 17.2 A. You can ignore any thermal expansion of the rod. Find (a) the resistivity at 20.0o C and (b) the temperature coefficient of resistivity at 20o C for the material of the rod.
ANSWER:Solution 11E
Step 1 of 5:
In the given problem, the length of the cylinder is L=1.5 m with diameter d=0.5 cm which is connected to potential V= 15 V across ends. The ammeter connected to it reads =18.5 A at temperature
and
=17.2 A at temperature
.
Here in part (a) we need to calculate the resistivity at using ohm’s law and resistivity equation. Where in part (b) we need to calculate the coefficient of resistivity at
for the given material of rod.
Given data,
- Length of cylinder, L=1.5 m
- Diameter of cylinder,d=0.5 cm
- Radius. r= d/2=0.25cm
-
Cross sectional area, A=
Using r = 0.25 cm =0.25 A=
A=19.625
-
Current at temperature
is
=18.5 A
-
Current at temperature
is
=17.2 A
- Voltage , V= 15 v
To find,
Resistance at ,
=?
Resistivity at ,
Coefficient of resistivity,