## 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