## 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