Ohm's Law and Resistivity

Which of the following is a statement of Ohm’s law?

• The resistance of a conductor is constant.

• The current in a conductor is inversely proportional to the potential difference across the conductor provided the temperature is constant.

• The resistance of a conductor is constant provided that the temperature is constant.

• The current in a conductor is linearly related to the potential difference across it.

The graph shows the variation of current I in a device with potential difference V across it. Which of the following statements is/are correct?

• The resistance of the device at P = 10 ohms.

• The resistance of the device increases with the p.d. across it.

• The device is ohmic.

• The resistance of the device = 0 ohm when there is no current passing through it.

Which of the following statements about electrical resistivity is/are correct?

• Metals usually have low electrical resistivity.

• The SI unit for electrical resistivity is ohm per metre

• The electrical resistivity of a material must increase with temperature.

• Changing the dimensions of a wire can vary its resistivity

In an experiment to determine the resistivity of a material, a student measures the resistance of several wires made from the pure material. The wires have the same length but different diameters. Which quantities should the student plot on the x-axis and the y-axis of a graph respectively to obtain a straight line?

• diameter² versus resistance

• diameter versus resistance

• diameter² versus 1/resistance

• diameter versus 1/resistance

A cylindrical resistor of volume V and length l has resistance R. The resistor has a uniform circular cross-section. What is the resistivity of the material from which the resistor is made?

•  $\frac{V}{Rl^2}$  

•  $\frac{V^2R}{l}$  

•  $\frac{VR}{l^2}$  

•  $\frac{V^2}{Rl}$  

A copper wire with length L and radius r has a resistance R.

What is the radius of a copper wire with length L/2 and resistance R?

• $2r$

• $\sqrt{2}r$

• $\frac{r}{\sqrt{2}}$

• $\frac{r}{2}$