## 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 × 12A = 144W

Exercise 1.3. Prove the formulas for series and parallel resistors

Exercise 1.4. Show that several resistors in parallel have resistance