## 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: $R=5k+10k=15k$ 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?

$R=\frac{V}{I}$ $\frac{12V}{1\Omega}=12A$ $P=VI$ $12V\times12A=144W$

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

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