Physics (2) Laboratory manual

PHYS 104 Laboratory Physics (2) Laboratory manual Dr. Chokri Belgacem, Dr. Yazid Delenda, Dr. Magdi Hasan Department of Physics, Faculty of Sciences and Arts at Yanbu, Taibah University - Yanbu Branch, KSA. yazid.delenda@yahoo.com Laboratory manual available from http://delenda.wordpress.com/teaching/phys104/ Contents 1 Introduction: Information and laboratory policy 2 2 Ohm s law 4 3 Wheatstone bridge 7 4 Capacitors 9 5 Kirchhoff s laws 12 6 Tangent Galvanometer 14 7 RC circuit in alternating current 16 1

1 Introduction: Information and laboratory policy 1.1 Supplies Students must bring the supplies they need, such as laboratory notebook(graph notebook), pencils, ruler, eraser and calculator, as these items are not provided in the laboratory. 1.2 Attendance Attending the laboratory session is compulsory. If the number of unexcused absences exceeds 3 or excused absences exceeds a further 2, a grade of DN will be assigned to the course. A student absent from a lab session with an official excuse is allowed to make-up the corresponding experiment. Unexcused absences will be dealt with at the discretion of the lab instructor. Students should prepare for the experiment in advance before coming to the lab. Students should arrive no later than 5 minutes of the beginning of the laboratory. 1.3 Evaluation The lab work compromises 25% of the total score of the course. The lab grade will be based on laboratory reports (10 marks) and a final laboratory exam (15 marks). The final laboratory exam contains both theoretical and practical parts. 1.4 Safety Students are required to leave the laboratory in a proper and clean state after they finish their experiment. NO FOOD OR DRINK IS ALLOWED IN THE LABORATORY A student must switch-off all electrical equipment in his possession after he finishes taking the measurements immediately, and disconnect the wires and components. Care must be taken with electrical equipment to avoid both damaging them and/or getting electrified. Do not overload an electrical device with more power than it can withstand. For instance a resistor that has a label of 4W may not be overloaded with a current and voltage such that P > 4W, where P = IV = I 2 R = V 2 /R. If in doubt always consult with your instructor. 1.5 Writing a laboratory report A typical laboratory report should contain the following items: aim, theory, equipment, procedure, a table of measurements, a graph (if required) and results and discussion (including conclusions). Laboratory reports must be submitted no later than the following week of performing the experiment. A student may not be allowed in the laboratory without a notebook. 2

1.6 Introduction to electrical measurements 1.6.1 Aim To teach students how to operate basic electrical measuring instruments such as am-meter and voltmeter, to use an analog multi-meter, a digital multi-meter, and an ohm-meter, to assess the precision of each of these measuring instruments, to set up a simple one-loop DC circuit and measure some of its characteristics 1.6.2 Equipment Am-meter, Voltmeter, Digital Multi-meter, DC power supply, resistors, switches, connecting cables. Note: This laboratory experiment consists only of demonstrations by the laboratory instructor followed by practice work by the students. No lab report needs to be written. 3

2 Ohm s law 2.1 Aim of the experiment The aim of this experiment is study Ohm s law as applied to a linear DC circuit. 2.2 Theory The resistance R of a conductor depends upon a number of factors including its nature, dimensions and even temperature. Most conductors have a constant resistance at constant temperature, so that the current I produced through the conductor is directly proportional to the voltage V across it. The relationship called Ohm s law states that I = V/R where R is a constant. The resistance R of the conductor is measured in Ohm (Ω), thus 1Ω = 1 V/A. The equivalent resistance R s of two resistors R 1 and R 2 connected in series, as shown in Figure 1, is given by R s = R 1 +R 2 R 1 R 2 Figure 1: Resistors in series or In the parallel configuration, shown in Figure 2, the equivalent resistance R p is given by 1 R p = 1 R 1 + 1 R 2 R p = R 1R 2 R 1 +R 2 2.3 Experimental Set-up The basic circuit used in this experiment comprises a DC power supply, an am-meter, a voltmeter and the resistor(s) to be studied, as shown in Figure 3. The am-meter (here a multi-meter is used as an am-meter) will measure the current I flowing through resistor R. It is therefore connected in series with the resistor. The voltmeter, which will measure the potential difference V across the resistor, is connected in parallel with the resistor. The polarities of the power supply must be respected or one would run the risk of damaging either the am-meter or the voltmeter, or both. 4

R 1 R 2 Figure 2: Resistors in parallel V A R + Figure 3: Experiment 1 2.4 Procedure: Part 1 measurement of a single resistance Connect the circuit as shown in Figure 3. R represents the unknown resistor provided. Switch on the power supply and vary the input voltage in regular steps between 0 and 5 volts. Record the voltage across R and the current I (tabulate your data in your notebook). Note: Do not use the screen on the power supply to read the voltage, use the voltmeter. Plot a graph of I versus V and verify that a straight line is obtained. Find the value of R from the slope of the graph. 2.5 Procedure: Part 2 measurement of resistance in series and parallel Connect two resistors R 1 and R 2 in series (see Figure 1) and, using the circuit shown in Figure 3, measure the current I for, say, five values of the voltage V (tabulate your data), and calculate the average value of the equivalent resistance R s. Connect R 1 and R 2 in parallel (see Figure 2) and, using the circuit shown in Figure 3, measure the current I for, say, five values of the voltage V, and calculate the average value of the equivalent resistance R p. 5

Using the known values of R 1 and R 2, calculate the equivalent series and parallel resistances, R s and R p using equations above and compare these results with those found here. Calculate the percentage difference between the calculated values and the experimental values (accuracy). Exercise Read the error off the resistors R 1 and R 2. Estimate the error in calculating both R p and R s. You may find the following useful: σ Rs = σr 2 1 +σr 2 2 σ 2 R p R 4 p = σ2 R 1 R 4 1 + σ2 R 2 R 4 2 6

3 Wheatstone bridge 3.1 Aim The aim of this experiment is to introduce bridge circuits and null detection method to measure the resistance of a conductor. 3.2 Theory Accurate measurements of an unknown resistance can be performed by comparing it with standard resistances (resistances which have been previously determined to sufficient accuracy) in some kind of bridge circuit, such as the Wheatstone bridge. The conventional diagram of a Wheatstone bridge is illustrated in Figure 4. A I 1 I 1 I D R 1 R 3 A R 2 R 4 C I I 2 I 2 B Figure 4: Wheatstone bridge in balance The combination is called a bridge because the am-meter is bridged between two parallel branches, DAC and DBC. The bridge is said to be balanced when the resistances are adjusted so that points A and B have the same potential, thus the current flowing between A and B is zero. This is indicated by a Digital Multi Meter reading zero. In practice, the current reading will swing between + and - values. When the bridge is balanced, the current I 1 through resistances R 1 and R 2 is the same, and current I 2 is the same in resistances R 3 and R 4. Since the points A and B have the same potential, the voltage across R 1 equals the voltage across R 3. Thus V DA = V DB and therefore: I 1 R 1 = I 2 R 3 (1) 7

Similarly the voltage across R 2 equals the voltage across R 4 (V AC = V BC ), so therefore Using these two equations we find that the currents cancel so that: which is the balance condition. Equation (3) could be written as I 1 R 2 = I 2 R 4 (2) R 1 R 2 = R 3 R 4 (3) R 1 = R 2 R 3 R 4 (4) Hence an unknown resistance may be measured by comparison with three known resistances. 3.3 Experimental setup The experimental set-up is shown in Figure 4. In this circuit the unknown resistance is R 1. R 2 is a known resistance, R 3 and R 4 are resistance boxes. 3.4 Procedure Connect the resistors provided in the circuit (see Figure 4). Obtain a rough idea of the resistance R 1 by making R 4 = R 2 Equation (4) indicates that balance is achieved when R 1 = R 3 in this case. Write down the value of R 3. This is the approximate value of R 1. The value you get from the previous step is not very accurate, but you can obtain a better estimate of R 1 by making R 4 = 10R 2. Again, vary R 3 until balance is obtained and then use the equation (4) to find the new value of R 1. Repeat step 4 by making R 4 = 100R 2. This gives the best value of R 1. Question: Can the accuracy of this bridge circuit be increased without limit? Make R 4 = 1000R 2 and try to find a balance. Record the value of R 1. 8

4 Capacitors 4.1 Aim The aim of this experiment is to measure the capacitance of a capacitor and to investigate the capacitance of capacitors in series and in parallel. 4.2 Theory The performance of many circuits can be predicted by systematically combining various circuit elements in series or parallel into their equivalents. For capacitors the equivalent capacitance for series and parallel combinations is as follows: C 1 C 2 C 3 C s C 1 C 2 C 3 C p Figure 5: capacitors in series and parallel 1 C s = 1 C 1 + 1 C 2 + 1 C 3 + C p = C 1 +C 2 +C 3 + where C s is the equivalent capacitance for the capacitors C i attached in series, and C p is that for the capacitors C i in parallel. 9

In the case of just two capacitors we simply have: C 1 C 2 C s = C 1 +C 2 (5) C p = C 1 +C 2 (6) If a capacitor is charged to a certain voltage, and then disconnected from the voltage source, the voltage on the capacitor will stay at the same value for a long time (determined by the leakage resistance of the capacitor). However, if the capacitance is connected to a resistance R, it will discharge; the time it takes to discharge is governed by R and C. Circuit theory indicates that the voltage at time t after the voltage source is disconnected is: V = V 0 e t/rc, (7) where V 0 is the initial voltage and e is the base of natural or logarithms, e = 2.71828. In this experiment we will measure the time constant of a capacitor, τ, that is, the time needed for the voltage to change from V 0 to V 0 /e 0.37V 0. This gives a direct measurement for the capacitance if the resistance R is known. From equation (7) the voltage at time t = RC is exactly V = V 0 e 1 = V 0 /e. Hence the time constant of a capacitor is just τ = RC. Note: RC has dimensions of time. Thus one may write 1Ω F = 1 s. 4.3 experimental set-up V R C Figure 6: experimental set-up 4.4 Part 1: Measuring the capacitance of a capacitor Connect the circuit shown in fig 6. 10

Turn on the power supply and adjust it until the voltmeter reads some convenient voltage, say 10 volts. This is V 0. disconnect the power and start the stopwatch. Measure the time for the voltage to fall from V 0 to V 0 /e (for V 0 = 10 V this is roughly 3.7 V). This is the time constant of the circuit Derive the capacitance of the capacitor (you can read off the resistance of the resistor or measure it using the multi-meter) You may repeat the measurement of the capacitance several times using various resistors, and then take the measured value to be the average. Compare your result with the true value of the capacitance and estimate the percentage accuracy. 4.5 Part 2: Capacitors in parallel Repeat the previous experiment with two capacitors connected in parallel and estimate the equivalent capacitance of the two capacitors experimentally by measuring the time constant. Compare your result with the theoretical value: and estimate the percentage accuracy. C p = C 1 +C 2 4.6 Part 3: Capacitors in series Repeat the previous experiment with two capacitors connected in series and estimate the equivalent capacitance of the two capacitors experimentally by measuring the time constant. Compare your result with the theoretical value: C s = C 1C 2 C 1 +C 2 and estimate the percentage accuracy. 11

5 Kirchhoff s laws 5.1 Aim The aim of this experiment is to study Kirchhoff s rules for loops and junctions, and measure the equivalent resistance of a network of resistors. 5.2 Theory Kirchhoff s rule for junctions states that the algebraic sum of currents into any junction is zero. Kirchhoff s rule for loops states that the algebraic sum of potential differences around any closed loop is zero. Consider the circuit shown in figure 7. I 1 I 1 +I 3 c R R I1 +I2 I 2 3R R I 3 5R I 2 I 3 I1 +I2 d + V Figure 7: Experimental setup The above circuit as drawn satisfies the first rule (junctions). Applying Kirchhoff s rule for loops we obtain three equations for three unknowns (I 1, I 2 and I 3 ) whose solutions is (see lectures) I 1 = 13 27R V 4 I 2 = 27R V 1 I 3 = 27R V We may also deduce that the equivalent resistance of the above network of resistors is: R eq = 27 17 R = 1.59R 12

5.3 Procedure The electrical circuit used in this experiment is shown in Figure 7. Set up the circuit shown in Figure 7. You will measure voltages and currents using a digital multi-metre. Your laboratory instructor will assign the value of R depending on the availability of resistors. Turnonthepowersupplyandselect V = 1.0V, asmeasuredbythemulti-metreinthevoltmeter function. At junction c or d remove the wires from resistors, one at a time, and measure the currents using the multi-metre in the am-metre function. When measuring the currents note we can define the current positive if the am-metre deflects upscale when the COM input is connected to junction c or d and the V-Ω-A input is connected to the resistor. 5.4 Analysis Using the value of R and V obtain the value of the current in each resistor (redraw figure 7 with the numerical value for each current). Compare the current in each resistor with that we obtained using Kirchhoff s rule. Does the sum of currents in each junction c or d equal to zero? What is the equivalent resistance of the network (the ratio V/I) experimentally (You may take several measurements and make a plot). 13

6 Tangent Galvanometer 6.1 Aim The aim of this experiment is to study the tangent galvanometer, measure the horizontal component of the earth s magnetic field. 6.2 Theory The earth exhibits a weak magnetic field at a given point on the earth s surface. This field has a horizontal component (parallel to the earth) and a vertical component (perpendicular to the earth). We will use an instrument, the tangent galvanometer, to measure the horizontal component of the field. 6.3 Method A coil subjects a compass needle to a magnetic field B c at right angles to the horizontal component of the earth s field B eh. The compass needle comes to rest along the resultant B = B eh + B c at an angle θ from North, where tanθ = B c B eh (8) (hence the name tangent galvanometer). This equation allows us to find B eh if we measure B c and B eh θ B B c Figure 8: The total magnetic field in the tangent galvanometer θ. 6.4 Data 1. Carefully measure and record d, the diameter of the coil. 2. Align the coil along the North-South axis using the compass needle as a guide. Turn the compass needle case until the compass needle points to 90, and the reading needle to 0. Do not disturb the alignment of the instrument for the rest of the experiment. 14

3. Hook up the circuit containing the tangent galvanometer using N = 50 turns tap of the coil. You will find that the components of the circuit influence the compass needle slightly. Try to minimise this effect by keeping the tangent galvanometer at a distance from them. 4. Turn on the power supply and vary the current and record the angle of deflection as current. 6.5 Calculations 1. Using the Biot-Savart law: B c = µ 0I 4π d l ˆr r 2, you can show that the field at the centre of the coil is given by B c = N µ 0I 2R (9) where R = d/2. Thus we may write: I = db eh µ 0 N tanθ 2. Plot I and a function of tanθ and find the slope A. 3. Deduce the magnitude of Earth s magnetic field: B eh = µ 0N d A 4. The accepted value of the horizontal component of the earth s field at Yanbu 1 is 0.33 10 4 T. What is the percent difference between your value and this value? 1 You may verify this at http://www.ngdc.noaa.gov/geomag/magfield.shtml. Use 24 26 30 N 38 3 39 E as coordinates for Yanbu. 15

7 RC circuit in alternating current 7.1 Aim The aim of this experiment is to study an RC circuit attached in series with an alternating current and measure the reactive impedance. 7.2 Theory The reactive impedance of an RC circuit (that is the ratio V rms /I rms, which ia a constant) is given by: ( ) 2 1 Z RC = R 2 + ωc where R is the resistance and C is the capacitance. Here ω is the angular frequency of the alternator: ω = 2πf with f the frequency. Calculate the estimated impedance for the resistor and capacitor provided. In Saudi Arabia, the value of f is 60 Hz. 7.3 Experimental setup Attach a resistor with a capacitor (in series) with the power source (set the current to AC and use the corresponding outputs). Attach two multi-metres as an am-meter to measure the rms current I rms and as a voltmeter to measure the rms voltage V rms across the circuit. Use a resistor 5MΩ with a capacitor 0.5 nf, or 2MΩ with 1 nf. 7.4 Data Take measurements of the variation of V rms as a function of I rms and plot your results in a graph and compute the slope (the impedance). How does your result compare with the theoretical expectation? (compute the percentage accuracy). 16