one or two sentences for each activity

Kirchoff’s Laws

Pre-Lab: Kirchoff’s Laws

Name: Section:

1. Solve the following set of three equations for the unknowns I1, I2, and I3 in terms of 1= 1.6 V, 2= 1.4 V, R1 = 220 , R2= 230 , and R3= 100 . Note: You will use the result during the lab (although the numbers may be different), so you should make a copy of your answer.

1− I2R2− I1R1 = 0

− 2+ I2R2− I3R3 = 0 I1 = I2+ I3

2. Briefly summarize the procedures you will follow in this lab. Write one or two sentences for each activity.

3. List any part (or parts) of the lab that you think may suffer from non-trivial experimental error, or may otherwise cause you trouble. How might this affect your results?

6

I have a strong resistance to understanding the relationship between voltage and current.

Anonymous

Objectives

• To find a mathematical description of the flow of electric current through different elements in direct current circuits (Kirchhoff’s laws).

• To gain experience with basic electronic equipment and the process of constructing useful circuits while reviewing the application of Kirchhoff’s laws.

Overview

Suppose we wish to calculate the currents in various branches of a circuit that has many components wired together in a complex array. In such circuits, sim- plification using series and parallel combinations is often impossible. Instead we can state and apply Kirchoff’s laws more formally to aid with the solution of such problems. These rules can be summarized as follows:

1. Junction (or Node) Rule (based on charge conservation): The sum of all the currents entering any node or branch point of a circuit (i.e., where two or more wires merge) must equal the sum of all currents leaving the node.

2. Loop Rule (based on energy conservation): Around any closed loop in a circuit, the sum of all emfs and all the potential drops across resistors and other circuit elements must equal zero.

81

82 Kirchoff’s Laws

Steps for Applying Rules

1. Assign a current symbol to each branch of the circuit and label the current in each branch I1, I2, I3, etc.; then arbitrarily assign a direction to each cur- rent. (The direction chosen for the circuit for each branch doesn’t matter. If you chose the “wrong” direction the value of the current will simply turn out to be negative.) Remember that the current flowing out of a battery is always the same as the current flowing into a battery.

2. Apply the loop rule to each of the loops by:

a) Letting the potential drop across each resistor be the negative of the product of the resistance and the net current through that resistor. Re- verse the sign to “plus” if you are traversing a resistor in a direction opposite that of the current.

b) Assigning a positive potential difference when the loop traverses from the (–) to the (+) terminal of a battery. If you are going through a battery in the opposite direction assign a negative potential differ- ence to the trip across the battery terminals.

3. Find each of the junctions and apply the junction rule to it. You can place currents leaving the junction on one side of the equation and currents com- ing into the junction on the other side of the equation.

In order to illustrate the application of the rules, let’s consider the circuit in the following figure.