# EXPERIMENT 12 OHM S LAW

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1 EXPERIMENT 12 OHM S LAW INTRODUCTION: We will study electricity as a flow of electric charge, sometimes making analogies to the flow of water through a pipe. In order for electric charge to flow a complete loop, called a circuit, must be established. A simple electrical circuit consists of three elements: 1. a source of electromotive force, such as battery 2. a load with a resistance, such as a lamp, which operates when a current flows through it, and 3. two or more conducting paths of negligible resistance (wires) which can be used to connect the source and the load in a closed loop. See figure 1. THEORY: Figure 1: A Simple Electrical Circuit. An electrical circuit transfers energy from one point to another, converging it from electrical energy to heat, light or mechanical energy. Here are some of the terms used to describe electric circuits. A source of electromotive force (emf) is some device in the circuit that produces a separation of (+) and (-) charges and in doing so provides the energy to move the charges around the circuit. A typical example is a battery that uses chemical energy to produce an emf. The unit of emf is the volt (V); 1 V = 1 J/C (Joule per coulomb). Current The battery is a source of DC (direct current) emf. The charge accumulates at the poles of the battery, indicated by the long (positive charge) and the short (negative charge) lines. In a DC circuit the current always flows in one direction, from the positive pole of the battery to the negative pole through the circuit. Electric current is the flow of charged particles, usually expressed as the amount of charge passing a given point per second. Usually these particles are negatively charged electrons. The unit of current is the coulomb per second, called an ampere (amp, symbolized by A). The amp is a large unit of current; we will often work in milliamps. Resistance is the opposition to the flow of current, and is measured in ohms (Ω), (1Ω = 1V/A). Resistance depends on several factors such as length, cross-sectional area, temperature and the type of material through which the charge is flowing. Some electrical devices (called resistors) are designed to have a large resistance.

2 As charge flows through a load (any part of the circuit that has a resistance is in general called a load; most often our loads will be resistors) energy is dissipated from the circuit, usually in the form of heat or light. The amount of energy dissipated by the load per coulomb of charge is known as the potential difference across the load. Potential difference has the same unit as emf, namely the volt, and gives a measure of energy dissipated in the load per coulomb of charge passing through it. We will sketch circuits using a set of standard figures, a few of which are shown below. In an AC (alternating current) source the current reverses direction over intervals of time. For example, the wall outlets of your home provide an AC current which switches direction 100 times each second. The ammeter and voltmeter are instruments used to measure current and voltage (either an emf or a potential difference) respectively. It is important that you become proficient with the use of these two instruments, as you will be using them quite often. There are two types of basic electric circuit, series and parallel. A circuit with only one conducting path is a series circuit. It can contain any number of loads and sources of emf. Figure 2 is a series circuit, shown schematically. C B A Figure 2: Schematic Diagram of Two Resistors in Series. There are no junctions allowing the current to split in a series circuit; all the elements are placed one after other. All the current must pass through the source and the resistor(s). Consequently, the current through each resistor is the same. For n resistors in series the current in every part of the circuit is the same, namely, I = I1 = I 2 = K = I n (Eq. 1) and the voltage across the group of n resistors is equal to the sum of the voltages across the individual resistors, namely, (Eq. 2) V = V1+ V2+ L + V n Using Ohm s law, V = IR, we find that the total resistance of the series group is equal to the sum of the individual resistance: 3) R= R1+ R2+ L + R n (Eq. A simple parallel circuit is shown in Figure 3. The opposite ends of each resistor have a common connection to the source. In this circuit the potential difference of each resistor is the same. Unlike the series circuit in a parallel circuit, there are one or more junctions that allow the current to split. Therefore, the current through each resistor need not be the same. A branch with B A C

3 high electrical resistance will have little electrical current passing through it, and a branch with low resistance will have a high current flowing through it. For n resistors in parallel connection, the voltage across each resistor is the same as that across any other resistor; this voltage is also the same as that across the entire group: (Eq. 4) V = V1= V2= L = V n and the total current is the sum of the separate currents, that is, (Eq.5) I = I1 + I 2+ L + I n Using Ohm s law we find that the reciprocal of the effective resistance of the group is equal to the sum of the reciprocal of the separate resistance: (Eq. 6) = + + L + R R1 R2 R n The product of the current and voltage gives the power dissipated in a resistor. THE EXPERIMENT: 1- Experimental Apparatus: Your lab station should be equipped with DC batteries, resistors, mutimeters, variable DC power supply, breadboard, banana cables, flat cables, and lamps. 2. EXPERIMENTAL PROCEDURE: Examine the multi-meter. Notice that it has a positive and negative terminal. When you measure the emf of a source you must be careful to observe these polarities; the positive terminal (or probe) should be connected to the positive terminal of the source. Likewise, the negative probe should be connected to the negative terminal of the source. The function key should be set to the desired V range. The polarity is also important when measuring the potential difference across a resistor. The positive probe must touch the end of the resistor with the highest potential (remember the current flows from plus to minus, with the potential Figure 4: Emf Measurement Figure 5: Current measurement.

4 decreasing at each resistor). Figure 4 shows the correct use of the voltmeter. As with the voltmeter, the polarity of the ammeter is also important. Current has to flow through the ammeter, so the circuit should be broken and the ammeter inserted into the circuit. Like the voltmeter, the positive probe goes to the point of highest potential. See Figure 5. A. Batteries in Series and in Parallel: With the two batteries mounted in their battery holders, measure the emf of one battery, then the emf of two batteries in series. When connecting batteries in series, connect them with the terminals as shown in Figure 6a. Figure 6: Terminal Connections for: a) Batteries in Series, b) Batteries in Parallel. Repeat with two batteries in parallel. Batteries connected in parallel are joined with the positive and negative terminals with common connections, as shown in Figure 6b. Summarize the results of these measurements on the worksheet in Table 1. B. Resistors in Series Next, construct the circuit of Figure 2, but complete the connections only when ready to take measurements. Open the circuit at point A to insert the ammeter in the circuit. Observe the proper polarity as discussed above. Measure and record the current going through the resistances in Table II. Then connect the voltmeter across the resistor at points A and B. Double check your work, referring to Figure 2. Before completing the connections have your lab instructor inspect the circuit. Measure and record the potential difference of the resistor. Repeat this measurement for the second resistor by inserting the ammeter in point B and the voltmeter between points B and C. Record the results in Table II. With the two resistors in series measure the voltage drop (potential difference) across the two resistors (connect the voltmeter between points A and C, i.e. V R1+R2 ). Record the value in Table II of your laboratory. In the same manner measure and record the current going through both resistors. C. Resistors in Parallel: Connect a single battery to two resistors in parallel as shown in Figure 3. Connect the voltmeter across the resistors at points A and B. Measure and record the voltage drop across each resistor in Table III.

5 By placing the ammeter in series with each one of the resistors, measure and record the current in Table III. With the two resistors in parallel record the current delivered by the battery to the resistors. When you are finished completely disconnect the batteries and resistors and using the ohmmeter measure the resistance of each resistor in the order used throughout the experiment and record your values in Table IV. Analysis: From Table II, add the values of V R1 + V R2 and compare the results with V R1+R2. From Table II compare the values of I 1 and I 2 with the total current leaving the battery. From Table III compare the value of the voltage delivered by the battery to the values of V R1 and V R2. From Table III, add the values of I R1 + I R2 and compare the results with I R1+R2. Calculate the total resistance for the series connection by using equation 3. Calculate the total resistance for the parallel connection by using equation 6.

6 EXPERIMENT 12 OHM S LAW NAME:. DATE:. SECTION:. THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION 1. EXPERIMENTAL PURPOSE: PHY 1400 LABORATORY REPORT State the purpose of the experiment.( 5 points ) 2. EXPERIMENTAL PROCEDURES AND APPARATUS: ) Briefly outline the apparatus used and the general procedures adopted. (5 points

7 3. RESULTS AND ANALYSIS TABLE I: (10 points) No. of EMF (V) Batteries SERIES PARALLEL 1 2 TABLE II: (20 points) No. of SERIES PARALLEL Resistors Potential Difference Across R 1 Current Potential Difference Across R Current TABLE III: (20 points) Potential Difference in Series Connection Current in Parallel Connection V R1 V R2 V R1+R2 I 1 I 2 I R1+R2 TABLE IV: Resistors Values as Measured With the Ohmmeter. (10 points) Measurements with R 1 R 2 OHMETER COLOR CODES Resistors in Series Analysis: (5 points) V R1 + V R2 = Comparison between V R1 + V R2 and V R1+R2 : Comparison between I 1 and I 2 with I R1+R2 : Resistors in Parallel Analysis: (5 points) I 1 + I 2 = Comparison between I 1 + I 2 and the total current leaving the battery:

8 Comparison between the value of the V R1 and V R2 and the voltage delivered by the battery: Calculations of total resistance for series connection: (10 points) Calculations of total resistance for parallel connection: (10 points)

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