ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ Purpose: The purpose of this lab is to explain and demonstrate the internal resistances of power supplies and batteries and why that is important. Background: When we use power supplies in the lab and batteries in our products we take for granted that these devices will give us accurate and steady voltage. In lab when we do our experiments or research we might easily conclude that the voltage the power supply says it is delivering to our circuit is what is displayed on its display, but after we are done with this lab you will always be skeptical of that and want to measure the voltage at the point of delivery. All power supplies and batteries have a source resistance which can affect the voltage which is delivered to the load. The goal of an ideal power source is to deliver all of its voltage to the source regardless of the current. We want our power sources to deliver a constant fixed DC voltage under all conditions (ideally). In an Ideal constant voltage source, there is no source resistance. Without a resistance in line with the load, all the voltage is delivered without any loss, no matter what the current (i.e. no I2R losses). But the best that can happen is to have this source or series resistance as low as possible and the best power supplies have series resistances much less than 1 ohm. When you look at the diagram below you see a voltage source with a series resistance driving a load resistance. Whenever you see two resistances like this there is a voltage divider. If our series resistance is very low (<<< RL) then most of the voltage of the source is delivered to the load. If the series resistance is higher then more voltage will be dropped across it depending on the current and less will be delivered to the load. Figure 1 power supply with its series resistance and load resistor, To be a constant voltage source: RL >>> Rs or Rs <<< RL Ideally Rs 0 so there is no concern about RL Important: What we will do in this lab is to calculate this hidden resistance in different voltage sources by making two measurements: open-circuit or unloaded voltage and closed-circuit or loaded voltage. Terms: Open Circuit or Un-loaded Voltage: This is the voltage measured when the power source is not connected to anything. Open circuit voltage allows us to determine the voltage of the source because with no current flowing through the resistor there is no loss or voltage drop across the resistor. Thus open circuit voltage equals source voltage. Load: A load is something connected to the circuit that draws current. Loaded: A circuit is said to be loaded when there is something connected to it that draws current like a resistor. Switch: A device which opens and closes a circuit if connected to two wires. Open position: The position of the switch where it is open (measures very high resistance). Closed position: The position of the switch where it is closed (measures very low resistance). ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ Figure 2: Why the open circuit voltage equals the source voltage. Figure 3: Loaded Voltage. Why some voltage can be lost in the power source. Supplies. One 24 ohm resistor Two NiMH Batteries AA size 1.2V Four headers 3 pin Four jumpers (use the cut wire kits not the premade jumpers) One switch Four double ended clip wires (2 red and 2 black) Be careful not to short the battery’s positive and negative terminals. Measuring the resistor and switch resistance. 1) Connect cables to the DMM and null out the resistance of the cables. 2) Measure the resistor’s exact value and record it here for later. ________ 3) Test the switch resistance a. You will have to find the right pins so you have an OPEN when it is not pressed b. and almost zero ohms when it is pressed or closed. c. Record the closed switch resistance: ____________ Setting up the test fixture we will use for the tests. 4) Push the DCV button to measure voltages. 5) Setup the breadboard with clip leads, jumpers, headers, switch and 24 ohm resistor to easily make some measurements: ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ We will setup a test fixture where connections from the batteries make it easy now to measure everything from the breadboard and allows you to change configurations very easily with everything on the breadboard. 1) Make sure that the switch is oriented correctly. a. The size of the switch is going to be bigger than what is shown but it will be connected centered over the trench on the breadboard as shown. This is a schematic of what we are doing above: When the switch is closed the battery is ‘loaded’ by the resistor and the voltage measurement of the battery will be different because of the current flowing through its series resistance. Note how the layout above follows the schematic. Raise your hand if you do not understand it. 1) Connect the clip-wires to the batteries, the jumper wires and the voltmeter cables to the breadboard as shown. 2) Make the connections using as shown below for measuring the loaded voltage of battery 1. a. Push the DCV button to make sure you will measure DC volts. b. When not pushing the switch the batteries are unloaded. i. The DMM displays the open circuit voltage. c. When the switch is pushed the battery will be loaded with the resistor. i. The DMM will display the loaded voltage. ii. Because the battery is loaded by the resistor this reading will change the longer you hold the switch, which is normal. So read the value quickly not waiting for it to stop. iii. You can measure a single value by pushing the “Single” button on the DMM (circled in the picture) while holding the switch on the breadboard. 1. If you used the Single button, pushing SHIFT AUTO/HOLD will bring it back to the scanning mode, displaying readings all the time. ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ 3) Enter the two values of the battery voltage: un-loaded (switch open) and loaded (switch closed) into the table below. 4) Measure each battery’s voltage by connecting a voltmeter’s red and black leads to their headers. a. Measure the unloaded voltage first and enter the value into the Open Circuit table below. It is important to use all the decimals on the DMM for this experiment to be the most accurate. b. To measure the loaded voltage, push the switch on the breadboard and then push the Single button. Enter that value in the Loaded Battery table below. c. Repeat steps a and b for Battery 2 after moving the DMM leads to its + and – terminals. i. Look at the schematic and try to figure out which wires to move to measure battery 2. ii. trace the + battery lead to the switch on your breadboard. iii. Do the same thing for the negative lead. iv. The lead to the resistor does not have to change. d. Be sure to record the battery unit number, written on the body of the battery, in the first table. If there is no battery number then write NA. Open Circuit Voltage (Switch open) Battery 1 #____ voltage (4 decimals) Loaded Circuit Voltage (Switch closed) Battery 1 voltage (4 decimals) Open Circuit Voltage (Switch open) Battery 2 #____ voltage (4 decimals) Loaded Circuit Voltage (Switch closed) Battery 2 voltage (4 decimals) Calculating Battery Rs The equation for calculating the Rs of the battery is derived from the circuit. One way to do this is to remember the voltage divider formula: 𝑅𝐿 𝑉𝐿 = 𝑉𝑜𝑐 (𝑅𝐿 + 𝑅𝑠 ) 𝑅𝑠 = 𝑅𝐿 (𝑉𝑜𝑐 − 𝑉𝐿 ) 𝑉𝐿 5) Calculate each battery’s Rs value based on the measurements you made above and fill in the table below: use your exact RL resistor value __________ measured above in #1. Battery 1 Rs value Battery 2 Rs value Measuring Series and Parallel battery voltages: Batteries may be connected in series or in parallel. When connected in series the voltages add but the current capacity remains the same. When connected in parallel the voltages remain the same but the current capacity doubles. ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ 6) Connect the two batteries in series using the guide below for how to do that on the breadboard. Note how the breadboard above is like the schematic below. Raise your hand if you do not understand. 7) Measure the series voltage open-circuit and loaded and enter the values into the table below. Series batteries (open circuit, switch open. 4 decimals) Series batteries (loaded, switch closed. 4 decimals) 8) Calculate the series Rs values using the formula above and your series measurements for Voc and VL. What was the difference between the series Rs value and the single Rs values? Explain any differences. ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ 9) Connect the batteries in parallel according to the diagram below: Note how the diagram above is like the schematic below. Raise your hand if you do not understand. 10) Measure the Parallel voltage open-circuit and loaded and enter the values into the table below. Parallel batteries (open circuit, switch open. 4 decimals) Parallel batteries (loaded, switch closed. 4 decimals) 11) Calculate the parallel Rs values using the formula above and your series measurements for Voc and VL. What was the difference between the parallel Rs value and the single Rs values? Explain any differences. Final Questions: 12) Derive the Rs formula from the voltage divider formula. Show your steps. ELE210U Batteries and Power Supply Source Resistance Lab R5 10 points Name _____________________ 13) Given that the internal resistance of the batteries is very low, how would you make the calculations more accurate knowing the switch resistance? Do you think we should consider the leads and connector resistances to? Should those be added to the load resistor? Answer in full sentences what you think. Extra Credit Problems: EC1: On your own, determine the Rs of our power supply outputs 1, 2 or 3 loaded with a 2 ohm resistor rated at 1W. Determine the voltage not to exceed 1W when loaded. o What is the voltage that will generate 1W with the 2 ohm resistor? o Use the P = V2/R to calculate this. o Enter that voltage on the power supply and fill-in the table below. o You will have to change the current to supply up to 1A or the results will not be correct. o Note: Do not use the breadboard for this test. Just use the test leads connected directly to the resistor. 2 pts Station # on bench PS Output # RL measured Vopen-ckt measured VLoaded measured Rs calculated The calculated Rs for the power supply should be in the mΩ or something is wrong and you will not get credit. EC2: Repeat the test on the same power supply output but at a higher voltage and power. Use a different power resistor to obtain a higher voltage to test at. Select one from the resistors available. Determine the voltage as done in EC1 to enter on the power supply and fill-in the table below. 2 pts Station # on bench PS Output # RL measured Vopen-ckt measured VLoaded measured Rs calculated The calculated Rs for the power supply should be in the mΩ or something is wrong and you will not get credit. EC3: Explain the Rs differences between the two voltage and current levels of the power supply observed in EC1 and EC2. 1 pt When finished set the current back to .1 A on the power supply and then push the voltage button so it is not set for current. Return all batteries, leads, resistors, and equipment back to the front. When returning the batteries make sure they are all oriented in the same direction in the holders to prevent short circuiting and catching fire.
