* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Title
Galvanometer wikipedia , lookup
Radio direction finder wikipedia , lookup
Integrating ADC wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Schmitt trigger wikipedia , lookup
Phase-locked loop wikipedia , lookup
Power electronics wikipedia , lookup
Power MOSFET wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Direction finding wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Wilson current mirror wikipedia , lookup
Surge protector wikipedia , lookup
Operational amplifier wikipedia , lookup
Current source wikipedia , lookup
Rectiverter wikipedia , lookup
Loop antenna wikipedia , lookup
Title of Experiment: Kirchhoff’s Course: Section: Name (s): Instructor: Date: Rules Gustav Robert Kirchhoff (1824-1887) – German Physicist Introduction and Objectives: Kirchhoff’s rules can be used to analyze complex circuits containing several resistors and voltage sources. There are two rules: i) The sum of currents entering any junction must equal the sum of the currents leaving that junction (this is also called the “junction rule”) ii) The sum of the potential differences across all the elements around any closed circuit loop must be zero (this is also called the “loop rule”) Equipment Required: Two 100 Ω and one 470 Ω resistor, current sensor or ammeter, voltage sensor or multi-meter, 3 1.5V batteries, battery connector, connecting wires. Lab Procedures: Set up a circuit as shown in the figure. Use batteries or a power supply for E1 and E2. Use resistors R1 (470 Ω), R2 (100 Ω) and R3 (100 Ω). Measure the actual voltages for each battery using a multi-meter or voltage sensor and record these values in Table 1. Using Kirchhoff’s rules, and the actual values of the voltages (E1 and E2) calculate the current in loops 1 and 2. Measure the actual values of the currents in each loop using an ammeter or current sensor. Enter your results in Table 1 and calculate the respective percent errors. R1 = 470Ω Loop 1 E1 = 3V Loop 2 R2= 100Ω I1 R3= 100Ω I2 E2 = 1.5V 1 Setting up the circuit: Ammeter E2 = 1.5V Loop 2 Loop 1 E1 = 3V 2 Close-up of resistors in circuit: R1 R3 R2 -ve 1.5V -ve 3V +ve 3V +ve 1.5V How to connect an ammeter: Positive lead going to ammeter/Curent sensor Negative lead from ammeter/ Current sensor 3 Table 1 Experimental values (measured by instruments): Current in loop 1 (i1) Current in loop 2 (i2) Voltage for battery 1 (E1) Voltage for battery 2 (E2) Calculations: Some guidelines to follow: i) Define a current i1 for loop 1 and i2 for loop 2. ii) The directions of the currents in these loops for calculation purposes is arbitrary. We can take either a clockwise direction or counterclockwise direction. In our figure, we choose the clockwise direction for the currents i1 and i2. iii) By convention if you move from the negative pole of a battery to the positive pole, the sign of the voltage is positive (because you are moving from a low voltage to a high voltage) and vice versa. iv) If you move in the same direction as the direction of the current, the sign of the voltage is negative, example –iR. R1 = 470Ω Loop 1 E1 = 3V Loop 2 R2= 100Ω i1 R3= 100Ω i2 E2 = 1.5V 4 Using the above conventions, and Kirchhoff’s loop rule (The sum of the potential differences across all the elements around any closed circuit loop must be zero), we can set up equations for the sum of voltages in each loop and equate them to zero: Loop1: +E1 - i1R1 –i1R2+i2R2 = 0 Substitute values for E1 and R into the above the equation: Equation I: Loop2: +E2 – i2R2 +i1R2-i2R3 = 0 Substitute values for E2 and R into the above the equation: Equation II: Now use Cramer’s rule to solve for i1 and i2: If: a1x + b1y = c1 a2x + b2y = c2 then: 5 Results: Using Kirchhoff’s Rules (Calculations): Current in Loop 1 Current in Loop 2 Using Ammeter/Current sensor: Current in Loop 1 Current in Loop 2 Use the formula for percent error to determine the percent error. (“A” = “Accepted” = values determined with Kirchhoff’s rules, (“E” = “Experimental” = values determined with Ammeter/Current sensor): Percent errors: Current in Loop1 Current in Loop2 Conclusions: 6