Question

A guage copper wire has a cross sectional area of 8.2×10-7 . It carries a current of 1.67A. Find 1.The magnitude of the electric field in the wire 2. The potential difference between two point on the wire 50.0cm apart 3. The resistance of a 50.0m length 4. Suppose the resistance of copper wire is 1.05 ohms at 20 degree centigrade. Find the resistance at 0 degree and 100 degree

Answer 1

1) The electric field inside the wire is zero.

2) The resistance of 50 cm piece of the wire is

$$R_{0.5}=\rho l/A=1.68\cdot10^{-8}\cdot0.5/(8.2\cdot10^{-7})=\\=0.01\space\Omega.$$

The potential difference is current times resistance:

$$V=IR=1.67\cdot0.01=0.0167\text{ A}.$$

3) The resistance of 50 meters is

$$R_50=\rho l/A=1.68\cdot10^{-8}\cdot50/(8.2\cdot10^{-7})=\\=1.024\space\Omega.$$

4) As we know, the resistance changes with temperature:

$$R(t)=R_0(1+\alpha T).$$

At 20°:

$$1.05=R_0(1+0.00393 \cdot20),\\ R_0=0.973\space\Omega.$$

Hence, at 0 degrees the resistance is 0.973 Ohms.

At 100°:

$$R(100)=0.973(1+0.00393\cdot100)=1.35\space\Omega.$$