Question

Solve the following problems.

1) Suppose that a resistor is connected to a 12.0-V battery through the simple circuit

shown in the diagram. Using Ohm’s Law, calculate the resistance of the resistor if

the current measured by the ammeter is:

a) 0.0364 A

b) 2.00 A

c) 0.00444 A

d) 0.240 A

e) 0.000120 A

2) In each case, calculate the resistivity of the material used for the resistor if the

resistor has a length of 0.00750 m and cross-sectional area of 0.00842 m2.

Answer 1

1) We will use Ohm's law:

$$R=\frac VI.$$

So, for each case:

a) 0.0364 A, R=330Ω

b) 2.00 A, R=6Ω

c) 0.00444 A, R=2700Ω

d) 0.240 A, R=50Ω

e) 0.000120 A, R=100000 Ω

2) The resistivity expressed in terms of resistance is

$$\rho=\frac{RA}{L}.$$

For each case:

$\text{a) }\rho=370\Omega·\text m\\ \text{b) }\rho=6.7\Omega·\text m\\ \text{c) }\rho=3030\Omega·\text m\\ \text{d) }\rho=56\Omega·\text m\\ \text{e) }\rho=112270\Omega·\text m\\$