## 1.2.2 Relationship between volage and current: resistors

**Exercise 1.1.** You have a 5k resistor and a 10k resistor. What is their combined resistance (a) in series and (b) in parallel?

In series:

*R* = 5*k* + 10*k* = 15*k*

In parallel:

$$R=\frac{1}{\frac{1}{5k}+\frac{1}{10k}}=\frac{1}{\frac{3}{10k}}=\frac{10k}{3}$$

**Execercise 1.2.** If you place a 1 ohm resistor across a 12 volt car battery, how much power will it disipate?

$$R=\frac{V}{I}$$

$$\frac{12V}{1\Omega}=12A$$

*P* = *V**I*

12*V* × 12*A* = 144*W*

**Exercise 1.3.** Prove the formulas for series and parallel resistors

**Exercise 1.4.** Show that several resistors in parallel have resistance