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=15kR=5k+10k=15k In parallel: R=115k+110k=1310k=10k3R=\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=VIR=\frac{V}{I} 12V1Ω=12A\frac{12V}{1\Omega}=12A P=VIP=VI 12V×12A=144W12V\times12A=144W

Exercise 1.3. Prove the formulas for series and parallel resistors

Exercise 1.4. Show that several resistors in parallel have resistance