# PHY 124 Lab 3 - DC circuits

If you need the .pdf version of these instructions you can get them here.

## Goals

The purpose of this laboratory is to observe the relationship between voltage drop across (not through), and current through (not across), electrical circuit elements. You will also gain familiarity with connecting circuits and with voltmeters (measuring voltage across a circuit element or elements-in-parallel) and ammeters (measuring current through a circuit element or elements-in-series). To help you in doing this laboratory, you should review the material in Ch. 17 of the online workshop notes for PHY 122; see also Chap. 22, Current and Resistance, and Chap. 23, Circuits, of KJF2: Knight, Jones, and Field, College Physics: A Strategic Approach, 2nd ed., the optional textbook for the course. If you don't have a copy, you will find one bolted to a desk in the Help Room, A-131 physics building. The Math/Physics Library on the “C” level of the physics building also has a few copies on closed reserve.

## Equipment

• 1 DC Power Supply
• 1 Voltmeter (yours may be different from the picture; use the DC volts setting)
• 1 Ammeter (yours may be different from the picture; use the DC amps setting)
• 1 board with resistive components
• 7 test leads (wires) with banana plugs
• 4 “alligator clip” clamps with banana sockets

Figure 1 is just below here

## Introduction

Ohmic components obey Ohm's law,

$\Large V=IR$
(3.1)

where V is voltage and I is current through a resistor with resistance R. Ohmic components will keep a constant resistance with varying voltage and current. This can be seen as a linear relationship on a V vs. I graph or an I vs. V graph. (Both kinds are commonly used.) Standard circuit resistors are ohmic. Other kinds of electrical components may not be and in these R may depend on factors such as the temperature (as it does in light bulbs), the direction of current flow (for example in diodes), or the light intensity falling on the component (light sensitive diodes).

You will use a voltmeter to measure V, the voltage drop across the component, and an ammeter to measure I, the current flow through the component. You must keep in mind that ammeters must be connected in series in circuits, while voltmeters must be connected in parallel across the circuit component whose voltage drop is to be measured. The figure below shows the proper setup.

Figure 2 is just above here

Technical note: non-zero meter readings are obtained only when some current flows through the meters. Hence, the meters have two connections. The current flowing through the meters influences the measurement. You want this effect to be very small. Thus “good” voltmeters have a large resistance compared to R, which allows only a small current to pass through. Since the voltmeter is in parallel to the resistor, the current through R is essentially determined by R and only a very small current flows through the voltmeter. The equivalent resistance of R and the voltmeter in parallel is close to the resistance of R because if $R_{voltmeter}>>R$ then $\frac{1}{R_{voltmeter}}+\frac{1}{R}\simeq\frac{1}{R}$. The voltmeter you use has the desired property i.e. it’s resistance is much larger than the resistance to be measured, R.

In an ideal case a “good” ammeter has a very small resistance compared to R, which allows current to easily pass through the ammeter and be measured. When this is the case and the resistor and the ammeter are in series, so the current measured in the ammeter is essentially determined by R. The equivalent resistance of R and the ammeter is close to resistance of R because if $R_{ammeter}< then $R+R_{ammeter}\simeq R$. This is only approximately true for the ammeter you will use in the lab. Because of this, the most significant source of error in this lab will come from the current measurements. Note that the voltmeter should not be connected across the (ammeter + resistor) together because the ammeter has a non-negligible resistance.

## Procedure

Before you start: Have your instructor measure the resistances of the resistors, which are next to each other on the board with the resistive elements shown below. You can also read the values of the resistor from their colored bands. (The instructions for doing this can be found here). Record the two resistances on your work sheet. These are your reference values and will be compared with your measured values. You can neglect the errors in the reference values as they will be much smaller than the errors in your measurements.

Figure 3 is just above here

### Part I-Ohmic Components

Our first measurement will be made on an ohmic component, the resistor $R_{2}$.

1. Make sure the power supply is switched off. Turn the black knob “Current ADJ.” all the way clockwise, and both the coarse and fine “Voltage ADJ.” knobs all the way counterclockwise to zero. Connect the power supply, ammeter, and voltmeter to the resistor (see Fig. 3) on your circuit board. Make sure you wire the setup exactly as shown in Fig 2. You can do this by visualizing and making two “loops” in your circuit. For the first loop, wire a circuit with the ammeter and the resistor in series: from the + terminal of the power supply to the red (high voltage) terminal of the ammeter; from the black (low voltage) terminal of the ammeter to the resistor; from the other end of the resistor (now its low voltage side) to the - terminal of the power supply. The next “loop” will involve connecting the voltmeter in parallel to the resistor. Wire the voltmeter from the high voltage terminal (red) of the voltmeter to the high voltage side of the resistor and from the low voltage terminal (black) of the voltmeter to the low voltage side of the resistor. The voltmeter should only be connected across the resistor if your set up is correct. Have your lab instructor “OK” your setup.

2. Switch the scales on your voltmeter to 20V and your ammeter to 0.2 A. You are going to investigate how voltage across R$_2$ changes with current through R$_2$. Increase the voltage, V, in 6 steps from ~ 5 to ~ 10 volts. For each voltage step, record the current, I (which is displayed in mA, but should be recorded in A), flowing through the resistor. Note that the left most knob (“course adjustment”) on the power supply is used to make large variations in the voltage V, and the middle knob (“fine adjustment”) is used for small adjustments. Neglect the error in V. For the error in I you can estimate the error as +/- 0.001 A because this is the last digit in the measurement displayed on the ammeter readout. Enter your measurements into the table on your worksheet.

3. You now need to plot your data using the plotting tool below. If we plot voltage vs current the slope of the graph should give us the value of the resistance. Make the plot and record your value for the resistance (with error) on your worksheet.

x axis label (include units):
y axis label (include units):
Check this box if the fit should go through (0,0).
(Don't include (0,0) in your list of points below, it will mess up the fit.)
What kind of errors are you entering below?
x1: +/-    y1: +/-
x2: +/-    y2: +/-
x3: +/-    y3: +/-
x4: +/-    y4: +/-
x5: +/-    y5: +/-
x6: +/-    y6: +/-
x7: +/-    y7: +/-
x8: +/-    y8: +/-
x9: +/-    y9: +/-

### Part II-Resistors in Series

In this part, we will connect and investigate two resistors in series. The equation for the total resistance of two resistors $R_{1}$ and $R_{2}$ in series is

$\Large R_{s}=R_{1}+R_{2}$
(3.2)

Use this equation to calculate the total resistance you should obtain when you connect your two resistors in series and write this value on your worksheet.

Wire the two resistors, $R_{1}$ and $R_{2}$, in series so that you obtain the following circuit.

Figure 4 is just above here

To do this, take the first circuit “loop” from Part I and add $R_{1}$ in series with $R_{2}$. Take the end of $R_{2}$ that was previously connected to the negative terminal of the power supply and connect it to one side of $R_{1}$. Then take the free end of $R_{1}$ and connect that end back to the power supply. Next, remake the second “loop” by connecting the voltmeter parallel to both $R_{2}$ and $R_{1}$. Wire the high voltage terminal (red) of the voltmeter to the high voltage side of $R_{2}$ and the low voltage terminal (black) to the low voltage side of $R_{1}$. Ask your instructor to check your wiring.

Once the resistors are wired correctly measure V and I with the voltage set to ~ 10 V. Calculate the measured resistance of the series combination using Ohm’s Law. Enter these values on your worksheet. Calculate the error $\Delta R_{s}$ of $R_{s}$ from the error in I, neglecting the error in V. Since $R_{s}=V/I$ the relative error of R is equal to the relative error in I (see expression (E.8) of Uncertainty, Error and Graphs).

Does the calculated value of the equivalent series resistance agree (within error) with the measured value?

### Part III-Resistors in Parallel

In this part, we have two resistors in parallel. The equation for the total resistance of resistors in parallel is

$\Large \frac{1}{R_{p}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$
(3.3)

Using this equation and the reference values for the resistors, calculate the expected value for the equivalent resistance $R_{p}$ of the parallel resistors and enter it in your worksheet.

Wire the two resistors, $R_{1}$ and $R_{2}$, in parallel.

Figure 5 is just above here

This will be slightly different than the last part and will consist of three “loops”. First, make the same first “loop” as in Part I. The second “loop” will be made by placing $R_{1}$ in parallel with $R_{2}$, which is in the first “loop”. To do this, connect one end of $R_{1}$ to the high voltage end of $R_{2}$ and the other end of $R_{1}$ to the low voltage end of $R_{2}$. Next you will make a third “loop” by putting the voltmeter in parallel with both $R_{1}$ and $R_{2}$. To do this connect the high voltage (red) terminal to the high voltage connection to which both $R_{1}$ and $R_{2}$ are wired. Do the same for the low voltage (black) terminal of the voltmeter and the low voltage connection to both resistors. Ask your instructor to check it.

Once the resistors are wired correctly, measure V and I at a voltage of ~10 V. Calculate the measured resistance of the parallel combination and its error from Ohm’s Law. Remember that as we neglect the error in the voltage, the relative error in R will be the same as the relative error in I. Enter your values in your worksheet. Calculate the error $\Delta R_{p}$ of the parallel resistance from the error in I neglecting the error of V as you did in Part II.

Does the calculated value of the equivalent parallel resistance agree (within error) with the measured value?

### Part IV-Non-ohmic Components

Repeat the procedure of Part I using the light bulb instead of the resistor. (You need to rewire the circuit so that it is like Fig 2, but with the light bulb in the place of $R_{2}$. Again, you will be looking at the relationship between V and I. You should see the bulb light up if you put a few volts across. If not, tighten the bulb. Take ~10 data points by varying V from ~1 to ~10V in reasonably uniform steps. Record each voltage and the associated current. Enter the measurements into the table on your worksheet. You do not need to record any errors for these data.

You should now enter the data into the table below. After you click 'submit', two plots will be produced, the first one is of voltage vs. current as we did for the ohmic resistor. You should find that this time the plot is not linear.

Voltage and Current Values
V1  V   I1  A
V2  V   I2  A
V3  V   I3  A
V4  V   I4  A
V5  V   I5  A
V6  V   I6  A
V7  V   I7  A
V8  V   I8  A
V9  V   I9  A
V10 V   I10 A

We can estimate the resistance at each point on the graph by making a linear approximation around each point. This means we take the change in voltage from the points on either side of the chosen point and divide by the change in current from the points on either side of the chosen point. For example, if I want to find the resistance at point n, I can approximate it as

$\Large R_{n}=\frac{V_{n+1}-V_{n-1}}{I_{n+1}-I_{n-1}}$
(3.4)

The computer will do this for you and make a plot of R vs. V.

Does the bulb behave as an ohmic resistor? Does the bulb resistance increase or decrease with temperature? Discuss with your partner and with the TA! 