DC C'rcuits Lab Instructions Objective: To predict the current through and the potential difference across several resistors in DC circuits and to conrm these experimentally. Theory: The current through a resistor is directly proportional to the potentiai difference ("voltage") across it and inversely proportional to its resistance: I=%orav=m This is Ohm's Law. We have also found the resistors in series or in parallel are equivalent to a resistance given by Series: Reg = R1 + Rg+,.. Parallel: it; 2 3+. + F++.. w .t This equivalent resistance aIIOWs us to use Ohm's Law to analyze circuits that contain more than one resistor. Good conductors, such as the copper in the wires we use to connect circuit eiements, have extremely low resistances So while not exactly zero, the resistance of a conductor is assumed to be so low compared to other resistances in the circuit that it can usually be considered to be zero. Therefore, the potential difference between two points in a continuous conductor can also be considered to be zero (this follows from AV 2 IR). This means that any two points along our connecting wires will be at the same potential. This is generally true even across connections between conductors. For example, two wires rmly connected together will be at the same potential for all points on eitherwire. This allows us to simplify our diagrams. So when two resistors are physically connected by conducting wires (shown in black} like this: All 01 these points are It the same potential they can be diagram med like this: \"1 a b R: All of these points are at the same potential This diagram makes the parallel nature of the connection clearer. Straight, neat iines to represent wires also make the diagram easier to read. Method: l have constructed two DC circuits containing a DC power supply and several resistors in series and/or in parallel. The resistances are labeled by color coded bars on the resistors and l have conrmed these using an ohmmeter. Also the overall potential difference for the circuit was measured using a voltmeten Using this information and Ohm's Law. we can predict what the currents in the resistors areas well as what the potential differences across these resistors are. We can then compare these predicted values with those measured by meters in the circuits, which are displayed in photos. Procedure: Circuit 1: 1. We will consider the following circuit: Vometer Power Supply voltmter (left) Ammeter {right Resistors which can be diagrammed as V Symbols used are: 'l l = battery or power supply W = resistor ammeter -G) =voltmeter Note that in the photo. the left end of R3 is connected at the voltmetervz. which is then connected to the negative end of the power supply. This is the same as if the resistor was connected directly to the power supply: all of these points are at the same potential. It was done this way to make the connections easier. The voltmeter V1 sits on top of the power supply and measures the voltage of the power supply. A1 gives the current leaving the power supply - all current leaving the power supply must pass through A1. Conrm that the circuit diagram accurately reects the physical circuit. From the enlarged photos below. read and record the value for the potential difference for the overall circuit from V1. Also record the resistances for resistors RA and RE which are written near the resistors. Note: These meters have two scales. Which scale is used is determined by which terminal is used for connections. I have chosen to use the upperilargeri scale on all meters because they give more appropriate ranges for the values in this experiment. The units for these measurements are written on the front of the meter, just under the scale. VI 10 DE VOLTA FISHER A 171.12 B2. It should also be noted that the ammeter itself has an internal resistance (we'll call this r). This is often assumed to be zero. but we want to include it in our analysis. Below is a photo of an ohmmeter measuring this resistance. The reading in Ohms is shown on the ohmmeter screen. Be sure to notice the decimal point. This resistance is small but not zero. Record the internal resistance of the ohmmeter. After making this measurement. the ohmmeter was disconnected and the ammeter was reconnected to the circuit. 'Il 'II l-.'..a"_.. II}lflfI}/////yl/ or. Hull-Ill!"- 3. Copy the circuit diagram above on paper, write in the values for V1 and all the resistances, including the internal resistance of the ammeter, and use these to analyze the circuit to nd the quantities listed below. Write your calculations and results clearly and neatly on blank paper and take images (scanning is best) and insert them into your lab report. Find: a. the equivalent resistance for all resistors together b. the expected current in the overall circuit c. the expected current through RB d. the predicted potential difference across RB. 3. We can now compare our calculations for b and d above with experimental values. Read and record the values from the ammeter A1 and the voltmeter V2 from the enlarged photos below: 4. Compare your expected values for from and AVE. (the potential difference across RB} with those read from the meters by calculating the percent differences. Circuit 2: 1. We will now consider the following circuit: The circuit diagram for this circuit is: RD RC Conrm that the circuit diagram accurately reects the physical circuit. From the enlarged photos below. read and record the value for the potential difference for the overall circuit from V1. Also record the resistances for all resistors. including the resistance of the ammeter (which is the same as in Circuit 1}. 3. Copy the circuit diagram above on paper. write in the values for V1 and all the resistances. including the internal resistance of the ammeter, and use these to analyze the circuit to nd the quanties listed below. Write your calculations and results clearly and neatly on blank paper and take images {scanning is best) and insert them into your lab report. Find: a. the equivalent resistance for all resistors b. the expected current in the overall circuit c. the expected current through R3 d. the potential difference across R3. 3' We can now compare our calculations of b and d above with experimental values. Read and record the values from the ammeter A1 and the voltmeter V2 from the enlarged photos below: 4. Compare your expected values for Item and AV\". l{the potential difference across R3} with those read from the meters by calculating the percent differences. Question: How much power was generated by RA in the second circuit while current was owing? Include this calculation in the work that you submit. Lab Report - DC Circuits Name: Date: Objective: Data Tables Circuit 1 Initial Values Calculated values From Meters RA RB Rey AVB % Diff I % Diff Circuit 2 Initial Values Calculated values From Meters VI RA RH Rc RD r Req Itotal AVB V2 % Diff Diff