# Week 5 (Sep. 23 - 27)

**Read:**This week I will be lecturing on electronic circuits. In particular, we will explore Ohm's law, electrical resistance, Kirchoff's rules of circuit analysis, and resistors and capacitors in parallel and series. In lab, we will learn how to build and analyze elementary electronic circuits using a digital multimeter.

**PHY 202 Lecture:**Drawing time-dependent electronic circuit diagrams, charging and discharging a capacitor, RC time-constant.

**Quiz:**Monday.

Homework:

Homework:

- High-voltage power lines deliver electrical current to your neighborhood. The aluminum wire used for these lines has a cross sectional area of about 5 square centimeters. What is the resistance of ten kilometers of this wire? Hint: you will need to look up the resistivity of aluminum.
**Answer: since the resistivity of Aluminum is 2.65e-8 Ohm-meters, we get a total resistance of 0.53 ohms** - A car battery has a rating of 220 ampere hours. This rating is one indication of the total charge that the battery can provide to a circuit before failing. What is the total charge (in coulombs) that this battery can provide? What is the maximum current that the battery can provide for 38 minutes.
**Answer: 220 amperes * 1 hour = 792,000 Coulombs. (You need to convert hours to seconds). Dividing this charge by 38 minutes we get a maximum current of 347 Amperes (this is huge).** - The current in a series circuit is 15.0 amperes. When an additional 8.00 ohm resistor is inserted in series, the current drops to 12.0 amperes. What is the resistance of the original circuit?
**Answer: since we are using the same battery, the voltage drop across the circuit is the same in both cases. So we know 15.0 amperes * R = 12.0 amperes * (R + 8). Solving for R, we get 32 ohms.** - Eight different values of resistance can be obtained by connecting together three resistors (1, 2 and 3 ohms) in all possible ways. What are they?
**All in series: 6 ohms; 3 in series with 1&2 in parallel: 11/3; 2 in series with 1&3 in parallel: 11/4; 1 in series with 2&3 in parallel: 11/5; 1 in parallel with 2&3 in series: 5/6; 2 in parallel with 1&3 in series: 4/3; 3 in parallel with 1&2 in series: 3/2; all three in parallel: 6/11** - Electromotive force and ohms law (ASGv3Ex25.1)
**Charging a capacitor**(PHY 202 students): Suppose a 12 volt battery is used to charge a 10 micro-farad capacitor through a 100 ohm resistor. (i) What is the final charge on the capacitor (after a very long time)? (ii) At what time will the capacitor be halfway charged?

**This week, we will learn (i) how to draw simple electronic circuit diagrams, and (ii) how to analyze electronic circuits using Kirchhoff's rules. We will use an adjustable DC power supply (0 - 6 Volts, 1 Amp), assorted resistors, a tungsten filament light bulb, and two digital multimeters that can measure electric potential (volts), current (amps) and resistance (ohms). The lab consists of three parts; these parts are described in detail in the DC Circuits laboratory . Here is a brief summary of the three parts. I'd recommend doing A and B in order, but part C can be done anytime.**

Laboratory:

Laboratory:

__Ohm's law for a resistor__. You will measure the current, I, passing through a resistor when a voltage V is applied across the resistor. Select a resistor of about 1000 Ohms. Be sure to set up your multimeters correctly so that one of them measures the voltage*across*the resistor (it acts as a voltmeter) and the other is in*series*with the resistor (it acts as an ammeter). Once you collect several data points (the more the better), make a plot of V vs. I. (Put V on the vertical and I on the horizontal axis) Is your data linear? If so, what is the slope? Is the slope equal to the resistance? There is a slight complication here: not all of the current measured by your ammeter is actually going through the resistor; a small portion of the current is being diverted into the voltmeter, which is in parallel with your resistor. How does this affect your measurements? In particular, are you*over*or*under*estimating the resistance of your resistor? And by how much? Compare your results to a calculation based on the*input impedance*of your voltmeter (look it up).__Ohm's law for a tungsten filament:__Repeat the previous measurements, but now use a small tungsten filament light bulb. To avoid burning out the bulb, you should put a resistor (try 50 or 100 Ohms) in series with the light bulb. The light bulbs are rated at 150 mAmp, so do not apply more than about 125 mAmps or they may burn out. Again, plot V vs I for your filament bulb. Is your plot linear? What does this imply?__Resistors in series and in parallel:__Now we will use a multimeter as an ohm-meter. Turn the knob to the appropriate setting. Select three resistors between 10 and 90 ohms. First, measure the resistance of each by itself. Does your reading correspond to the color code on the resistor? Second, put the resistors in series and measure the resistance. Is it what you'd expect? Finally, put the resistors in parallel and measure the resistance. Is it what you'd expect?