Kirchhoff’s Laws

Name: _____________________

Objective

To understand Kirchhoff’s circuit rules and use them to determine the currents that flow in various parts of DC circuits.

Overview

Consider a circuit that has many components wired together in a complex array. Suppose you want to calculate the currents in various branches of this circuit. The rules for combining resistors are convenient in circuits made up only of resistors that are connected in series or in parallel. While it may be possible in some cases to simplify parts of a circuit with the series and parallel rules, complete simplification to an equivalent resistance is often impossible. The application of Kirchhoff’s rules can help us to understand complex circuits with more than one battery.

Kirchhoff circuit rules applied to circuits are based on two conservation laws – conservation of energy and conservation of charge. To analyze the circuits, we define few terms:

Branch: A branch is a portion of the circuit in which the current is the same through all the circuit elements.

Junction or Node: A junction in a circuit is a place where two or more wires are connected. It is the point of connection between two or more branches.

Loop: A loop is any closed path in a circuit.

Kirchhoff’s rules:

Junction Rule: The sum of the currents entering a junction equals the sum of the currents leaving out of the same junction. Junction rules is based on charge conservation.

Loop Rule: The sum of the changes in electric potential around a closed loop is zero.

Let us consider the circuit shown below.

Question 1-1: How many unknown currents are flowing in the circuit?

Question 1-2: Mark Junction (or Junctions) on the figure.

We will use PHET simulation Circuit Construction Kit: DC – Virtual Lab (https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab)

Open the PHET simulation Circuit Construction Kit: DC – Virtual LabSet-up the circuit shown in the above figure.

Set the resistances values: R1 = 75 W, R2 = 40 W, and R3 = 100 W. Click on the resistor; you will be able to see the value of resistance and then change it using the slider switch.

Choose the following battery voltages: ℇ1=10 V and ℇ2=25 V Take a screenshot after you connect the circuit and paste it.

Question 1-3: Apply Junction rule to one of the junctions. Do you get a different equation when you apply the rule to the other junction?

Equation 1:

Question 1-4: Assuming that the internal resistances of the batteries are negligible, apply loop rule to any two closed loops. Write down the equations for each loop.

Equation 2:

Equation 3:

Solve these three equations for the three unknown currents, I1, I2, and I3 in amperes. Show your calculations below.

Modify the circuit to measure currents flowing through each resistor. You must use ammeter to measure current.

Take a screenshot after you connect ammeters in the circuit and paste it below.

Vary the battery emf E1 and complete the table below:

Calculate the currents flowing through each resistor using Ohm’s law, V = IR

E1(V) E2(V) V1

(V) V2

(V) V3

(V) I1

(A) I2

(A) I3

(A) I1 (calculated) I2 (calculated) I3

(calculated)

10 25

15 25

20 25

25 25

30 25

Question 1-5: Did your measured currents match with the calculated current values?

Question 1-6: Use your measured current values to verify the junction rule at the junction in the circuit. Show one calculation.

Question 1-7: Use your measured voltage values to verify the loop rule in the left loop of the circuit. Show one calculation.

Question 1-8: Why aren’t the resistors R1 and R2 in series? Why aren’t they in parallel?

Now consider the case where resistor R2 is removed from the circuit. Take a screenshot after you have made the changes.

Question 1-9: Will you need to generate more or fewer equations with Kirchhoff’s loop rule? With Kirchhoff’s Junction rule? Why?

Question 1-10: What is the effective value of R2 in the modified circuit?