# Differences

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phy124summer:lab_3 [2010/07/13 16:15] (current)
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+<​html><​STYLE>​ #​jsMath_Warning {display: none} </​STYLE></​html>​
+
+====== PHY 124 Lab 3 - DC circuits======
+
+[[http://​www.ic.sunysb.edu/​Class/​phy122ps/​labs/​dokuwiki/​pdfs/​124lab3worksheet.pdf|Important! You need to print out the 2 page worksheet you find by clicking on this link and bring it with you to your lab session.]]
+
+
+If you need the .pdf version of these instructions you can get them [[http://​www.ic.sunysb.edu/​Class/​phy122ps/​labs/​dokuwiki/​pdfs/​phy124lab3.pdf|here]].
+
+===== Goals =====
+The purpose of this laboratory is to observe the relationship between voltage drop across, and current through, electrical circuit components. ​ You will also gain familiarity with connecting circuits and with voltmeters (measuring voltage) and ammeters (measuring current).
+
+
+===== Video =====
+<​flashplayer width=640 height=480>​file=http://​www.ic.sunysb.edu/​Class/​phy122ps/​labs/​phy122vid/​phy124lab3.flv</​flashplayer>​
+
+===== Equipment =====
+
+  * 1 DC Power Supply
+  * 1 Voltmeter
+  * 1 Ammeter ​
+  * 1 board with resistive components
+  * 7 wires
+  * 4 clamps
+
+{{124l3fig1.jpg}}
+
+===== Introduction =====
+
+Ohmic components obey Ohm's law,
+
+
+<WRAP column 35%>\\
+</​WRAP>​
+<WRAP column 45%>
+$\Large V=IR$
+</​WRAP>​
+<WRAP column 10%>
+(3.1)
+</​WRAP>​
+\\
+
+
+ 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. 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 sketch below shows the proper setup.
+
+{{124l3fig2.jpg?​400}}
+**Fig 2**
+
+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 $R_{ammeter}<<​R$ 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 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 [[http://​en.wikipedia.org/​wiki/​Electronic_color_code|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.
+
+{{124l3fig3.jpg?​600}}
+**Fig 3**
+
+==== Part I-Ohmic Components ====
+
+Our first measurement will be made on a 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 changes with current. ​ 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.
+
+<​html>​
+<form method="​post"​ action="​http://​mini.physics.sunysb.edu/​~mdawber/​plot/​124lab3plot.php"​ target="​_blank">​
+x axis label (include units): <input type="​text"​ name="​xaxis"​ size="​60"/><​br>​
+y axis label (include units): <input type="​text"​ name="​yaxis"​ size="​60"/><​br>​
+Check this box if the fit should go through (0,​0). ​ <input type="​checkbox"​ name="​zero"​ value="​y"​ /><​br>​
+(Don't include (0,0) in your list of points below, it will mess up the fit.)<​br>​
+What kind of errors are you entering below?<​SELECT name="​errortype">​
+<OPTION value="​none">​None</​OPTION>​
+<OPTION value="​x">​Errors in x</​OPTION>​
+<OPTION value="​y">​Errors in y</​OPTION>​
+<OPTION value="​xy">​Errors in x and y</​OPTION>​
+</​SELECT>​
+<br>
+
+x1: <input type="​text"​ name="​x1"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx1"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y1:  <input type="​text"​ name="​y1"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy1"​ size="​10"/><​br/>​
+x2: <input type="​text"​ name="​x2"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx2"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y2:  <input type="​text"​ name="​y2"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy2"​ size="​10"/><​br/>​
+x3: <input type="​text"​ name="​x3"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx3"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y3:  <input type="​text"​ name="​y3"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy3"​ size="​10"/><​br/>​
+x4: <input type="​text"​ name="​x4"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx4"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y4:  <input type="​text"​ name="​y4"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy4"​ size="​10"/><​br/>​
+x5: <input type="​text"​ name="​x5"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx5"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y5:  <input type="​text"​ name="​y5"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy5"​ size="​10"/><​br/>​
+x6: <input type="​text"​ name="​x6"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx6"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y6:  <input type="​text"​ name="​y6"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy6"​ size="​10"/><​br/>​
+x7: <input type="​text"​ name="​x7"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx7"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y7:  <input type="​text"​ name="​y7"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy7"​ size="​10"/><​br/>​
+x8: <input type="​text"​ name="​x8"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx8"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y8:  <input type="​text"​ name="​y8"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy8"​ size="​10"/><​br/>​
+x9: <input type="​text"​ name="​x9"​ size="​10"/>​+/​-<​input type="​text"​ name="​dx9"​ size="​10"/>&​nbsp;&​nbsp;&​nbsp;​ y9:  <input type="​text"​ name="​y9"​ size="​10"/>​+/​-<​input type="​text"​ name="​dy9"​ size="​10"/><​br/>​
+<input type="​submit"​ value="​submit"​ name="​submit"​ />
+</​form>​
+</​html>​
+
+==== 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
+
+<WRAP column 35%>\\
+</​WRAP>​
+<WRAP column 45%>
+$\Large R_{s}=R_{1}+R_{2}$
+</​WRAP>​
+<WRAP column 10%>
+(3.2)
+</​WRAP>​
+\\
+
+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.
+
+{{124l3fig4.jpg}}
+
+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 “EU”).
+
+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
+
+<WRAP column 35%>\\
+</​WRAP>​
+<WRAP column 45%>
+$\Large \frac{1}{R_{p}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$
+</​WRAP>​
+<WRAP column 10%>
+(3.3)
+</​WRAP>​
+\\
+\\
+
+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 on your worksheet. ​
+
+Wire the two resistors, $R_{1}$ and $R_{2}$, in parallel. ​
+
+
+{{124l3fig5.jpg}}
+
+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 from Ohm’s Law and its error. ​ 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 on 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. Record each voltage and the associated current. ​ Enter the measurements into the table on your worksheet. You do not need to record any errors are needed for this data.
+
+You should now enter the data in to the table below. When you click submit two plots will be produced, ​ the first one is of voltage against current as we did for the ohmic resistor. You should see that this time the plot is not linear. ​
+
+
+<​html>​
+<form method="​post"​ action="​http://​mini.physics.sunysb.edu/​~mdawber/​plot/​124lab3.php"​ target="​_blank">​
+
+
+Voltage and Current Values <br/>
+V1&​nbsp;​ <input type="​text"​ name="​V1"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I1&​nbsp;​ <input type="​text"​ name="​I1"​ size="​10"/>​ A <br/>
+V2&​nbsp;​ <input type="​text"​ name="​V2"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I2&​nbsp;​ <input type="​text"​ name="​I2"​ size="​10"/>​ A <br/>
+V3&​nbsp;​ <input type="​text"​ name="​V3"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I3&​nbsp;​ <input type="​text"​ name="​I3"​ size="​10"/>​ A <br/>
+V4&​nbsp;​ <input type="​text"​ name="​V4"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I4&​nbsp;​ <input type="​text"​ name="​I4"​ size="​10"/>​ A <br/>
+V5&​nbsp;​ <input type="​text"​ name="​V5"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I5&​nbsp;​ <input type="​text"​ name="​I5"​ size="​10"/>​ A <br/>
+V6&​nbsp;​ <input type="​text"​ name="​V6"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I6&​nbsp;​ <input type="​text"​ name="​I6"​ size="​10"/>​ A <br/>
+V7&​nbsp;​ <input type="​text"​ name="​V7"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I7&​nbsp;​ <input type="​text"​ name="​I7"​ size="​10"/>​ A <br/>
+V8&​nbsp;​ <input type="​text"​ name="​V8"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I8&​nbsp;​ <input type="​text"​ name="​I8"​ size="​10"/>​ A <br/>
+V9&​nbsp;​ <input type="​text"​ name="​V9"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I9&​nbsp;​ <input type="​text"​ name="​I9"​ size="​10"/>​ A <br/>
+V10 <input type="​text"​ name="​V10"​ size="​10"/>​ V&​nbsp;&​nbsp;&​nbsp;​I10 <input type="​text"​ name="​I10"​ size="​10"/>​ A <br/>
+
+<input type="​submit"​ value="​submit"​ name="​submit"​ />
+</​form>​
+</​html>​
+
+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 point and divide by the change in current from the points on either side of the point. For example if I want to find the resistance at point n I can approximate it as
+
+<WRAP column 35%>\\
+</​WRAP>​
+<WRAP column 45%>
+$\Large R_{n}=\frac{V_{n+1}-V_{n-1}}{I_{n+1}-I_{n-1}}$
+</​WRAP>​
+<WRAP column 10%>
+(3.4)
+</​WRAP>​
+\\
+\\
+
+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 TA!
+