Computer Science homework help

PHYS 1402 Lab – 7: 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. Computer Science homework help

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.

Figure 1

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

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

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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 Lab
Set-up the circuit shown in the above figure -1.
Set the resistances values: R₁= 75 W, R₂ = 40 W, and R₃= 100 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:

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

Question 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 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. Computer Science homework help

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.
Set battery emf= 10 V and note down the voltage across each resistor (V₁, V₂, and V₃) using voltmeter in the table below. Note the currents flowing through each resistor (I₁, I₂, and I₃) using ammeter. Ammeter must be connected in series to the resistor.
Vary the battery emf. Each you vary battery emf note down the voltage across each resistor and currents flowing through each resistor in the table below.
Using Ohm’s law, V = IR, calculate the currents flowing through each resistor.

I₁ (calculated) = V₁/ R₁; I₂ (calculated) = V₂/ R₂; I₃ (calculated) = V₃/ R₃

(V)	(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 5: Did your measured currents match with the calculated current values?

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

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

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

Question 9: Determine the current and its direction, in each resistor, for the circuit shown below. Show your calculations. Computer Science homework help

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