Electrical Engineering: Basic Laws (9 of 31) Kirchhoff's Laws: A Simple Example

Summary

This lecture provides an introduction to using Kirchhoff's laws in simple electrical circuits, particularly focusing on a series loop circuit. The instructor explains the concept of series circuits, node sharing, and reference voltage using ground. They calculate current using Ohm's law, showing how Kirchhoff’s Voltage Law (KVL) applies by summing voltages around the loop, which should equal zero. The example highlights the simplicity of using Ohm’s law in such circuits but emphasizes that Kirchhoff’s laws are crucial for solving more complex circuits with multiple branches and voltage sources.

Takeaways

• 🔄 The circuit discussed is a simple series loop where all components are connected in series, meaning each component shares only a single node with another component.
• ⚡ The circuit is connected to ground, which serves as a reference point set to zero volts, ensuring consistent voltage measurements.
• 🔋 The lecture explains the process of summing voltages around a loop using Kirchhoff's Voltage Law (KVL), stating that the sum of all voltages should equal zero.
• 📐 Kirchhoff’s Current Law (KCL) is mentioned, but since there’s only one loop, it’s not essential for this simple circuit as the current is the same throughout.
• 📏 Ohm's Law (V = IR) is used to calculate the current in the circuit, given that the total voltage is 40 volts and the total resistance is 10 ohms (R1 + R2).
• 💡 The calculated current in the circuit is 4 amps, based on the total resistance and voltage.
• ➖ When calculating the voltage drops across each resistor, the first resistor (2 ohms) results in an 8-volt drop, and the second resistor (8 ohms) causes a 32-volt drop.
• ✅ Verifying Kirchhoff's Voltage Law, the voltage rise across the battery is 40 volts, and the sum of the voltage drops across the resistors (8V + 32V) equals this rise, satisfying KVL.
• 🔧 While KVL is useful in this basic example, the video notes that Kirchhoff's Laws become essential in more complex circuits with multiple branches and voltage sources.
• 🧠 The lecture demonstrates that Kirchhoff’s Laws, combined with Ohm's Law, can simplify the analysis of circuits, especially in more complex situations.

Q & A

What type of circuit is being discussed in the script?

The script discusses a series circuit, where all components are connected in series, meaning any two components share a single node between them that is not shared by any other component.

What is the significance of connecting the circuit to ground?

Connecting the circuit to ground means that a part of the circuit is at zero volts, serving as a reference voltage. This is done by connecting the circuit to a conductive material that can absorb or release charges to maintain this zero-volt condition.

How is Kirchhoff's Voltage Law applied in this circuit?

Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around a closed loop must equal zero. In the script, the sum of the voltage rise across the battery and the voltage drops across the resistors is shown to equal zero, confirming KVL.

How do you calculate the current in a series circuit using Ohm’s Law?

In a series circuit, the current can be calculated using Ohm’s Law (I = V/R). Here, the total resistance is the sum of all resistances in the circuit, and the current is equal to the total voltage divided by the total resistance.

What are the voltage drops across the resistors in the example circuit?

In the example circuit, the voltage drop across the first resistor (R1 = 2 ohms) is 8 volts, and the voltage drop across the second resistor (R2 = 8 ohms) is 32 volts.

Why is Kirchhoff’s Current Law not very useful in this example?

Kirchhoff’s Current Law (KCL) is not very useful in this example because there is only one current flowing through the entire series circuit, meaning the current entering and leaving each node is the same, so KCL doesn't provide additional insights.

What is the total resistance in the example circuit?

The total resistance in the example circuit is the sum of the two resistors, R1 and R2. Therefore, the total resistance is 2 ohms + 8 ohms = 10 ohms.

How much current flows through the circuit in the example?

The current flowing through the circuit is calculated as I = V / (R1 + R2) = 40 volts / 10 ohms = 4 amps.

Why is Kirchhoff’s Voltage Law important in circuit analysis?

Kirchhoff’s Voltage Law is important because it allows you to verify that the sum of all voltage rises and drops around any closed loop in a circuit equals zero, ensuring energy conservation and helping in analyzing complex circuits.

When would Kirchhoff’s Laws be more useful in circuit analysis?

Kirchhoff’s Laws become much more useful when analyzing complex circuits with multiple branches, voltage sources, and current paths. They help in calculating the currents and voltages across different parts of the circuit in such cases.

Outlines

00:00

🔌 Introduction to Simple Loop Circuit

This paragraph introduces a simple loop circuit example. It explains that all components in this series circuit are connected in such a way that each component shares a single node with only one other component. The paragraph mentions the significance of ground, which is used as a reference voltage of 0 volts, achieved by connecting it to a conductive material. The primary focus is on summing voltages in the loop to verify that they add up to zero.

🔄 Kirchhoff’s Current Law and its Application

The paragraph explores Kirchhoff’s Current Law (KCL), stating that the current entering a node must equal the current leaving it. In the case of this circuit, a single current flows throughout, making KCL less useful here. The author suggests using Ohm’s Law (I = V/R) to calculate current instead, as this method provides the needed values for simple circuits like this one.

📏 Applying Ohm's Law to Calculate Current

Here, Ohm’s Law is applied to the circuit. The voltage is 40 volts, and the resistors in series have values of 2 ohms and 8 ohms. By adding the resistances and dividing the total voltage by the total resistance, the current is calculated to be 4 amps. This direct use of Ohm’s Law makes it unnecessary to apply Kirchhoff’s Laws for this simple circuit.

🔋 Verifying Kirchhoff’s Voltage Law

The focus shifts to verifying Kirchhoff’s Voltage Law (KVL), which states that the sum of voltages around a loop must equal zero. The author walks through a clockwise loop starting from a node and examines the voltage rise across the battery and the voltage drops across the resistors. By inserting the current value and resistance, the calculations show that the sum of the voltages equals zero, validating KVL.

📊 Voltage Drop Calculation

In this section, the actual voltage drops across the resistors are calculated. The first resistor has a voltage drop of 8 volts, and the second resistor has a drop of 32 volts. When subtracted from the battery’s 40 volts, this confirms that the total equals zero, providing further proof that Kirchhoff’s Voltage Law holds in this circuit.

🔗 The Importance of Kirchhoff’s Laws in Complex Circuits

The paragraph concludes by highlighting that while Kirchhoff’s Laws might not be essential for simple circuits like the one discussed, they are crucial for more complex circuits involving multiple branches and voltage sources. In these cases, Kirchhoff’s Laws are indispensable for solving currents and voltages throughout the circuit.

Keywords

💡Kirchhoff's Laws

Kirchhoff's Laws are fundamental principles used to analyze electrical circuits. The video explains two key laws: Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL). KVL states that the sum of voltages around a closed loop must equal zero, while KCL states that the current entering a node must equal the current leaving it. These laws help in determining current and voltage in more complex circuits.

💡Series Circuit

A series circuit is a type of electrical circuit where components are connected end-to-end, meaning the current flows through each component one after the other. The video uses a series circuit to demonstrate the application of Ohm’s Law and Kirchhoff's Laws, emphasizing that the same current flows through all components since they share nodes exclusively with their neighbors.

💡Ohm's Law

Ohm's Law is a basic rule in electrical circuits that states that current (I) is equal to voltage (V) divided by resistance (R), or I = V/R. The video uses this law to calculate the current flowing through a simple loop circuit by dividing the voltage (40V) by the total resistance (10 ohms). This helps explain how current behaves in the example circuit.

💡Voltage

Voltage refers to the potential difference between two points in a circuit, which drives the flow of electric current. In the video, the voltage of 40V is provided by a battery, and it is used to calculate the current and verify Kirchhoff’s Voltage Law by adding up the voltage drops across resistors and comparing them to the total voltage.

💡Current

Current is the flow of electric charge through a circuit. The video calculates a current of 4 amps by applying Ohm’s Law to the series circuit. It also highlights how Kirchhoff’s Current Law applies, explaining that the current entering and leaving any node must be equal in this particular example.

💡Resistance

Resistance opposes the flow of current in a circuit. In the video, two resistors with resistances of 2 ohms and 8 ohms are used in series. Their combined resistance (10 ohms) is used to calculate the current in the circuit. Resistance also affects the voltage drop across each resistor, which is a key part of the Kirchhoff’s Voltage Law example.

💡Node

A node in an electrical circuit is a point where two or more circuit elements meet. In the video, several nodes are identified, with the explanation that at each node, the current entering must equal the current leaving (Kirchhoff’s Current Law). This concept is important for analyzing complex circuits with multiple branches.

💡Ground

Ground refers to a reference point in the circuit that is considered to have zero voltage. In the video, the circuit is connected to ground, establishing a common reference for measuring voltage. Grounding is important in both theoretical calculations and practical circuit designs to ensure consistency in voltage measurements.

💡Voltage Drop

A voltage drop occurs when electrical energy is lost as current flows through a resistor or another component. In the video, the voltage drop across two resistors is calculated as 8V and 32V, respectively. The sum of these voltage drops equals the total voltage supplied by the battery, demonstrating Kirchhoff’s Voltage Law in action.

💡Closed Loop

A closed loop is a path in a circuit where the current can travel in a complete circle, returning to its starting point. In the video, the circuit forms a simple closed loop, and Kirchhoff’s Voltage Law is applied by summing all voltage changes around the loop, confirming that they equal zero, as expected in any closed-loop circuit.

Highlights

Introduction to using Kirchoff's laws in circuit analysis.

Explanation of a simple loop circuit with components connected in series.

Series circuit defined: any two components share a single node between them, not shared by other branches.

Ground reference in a circuit means zero volts, set by connecting to a metal object to draw current or charge.

Kirchhoff's Voltage Law (KVL): sum of all voltages around a loop should equal zero.

Discussion of using Ohm’s Law to find current in the circuit (I = V/R).

Example calculation: with a 40V source and two resistors (2Ω and 8Ω), current equals 4 amps.

Application of Kirchhoff's Current Law (KCL): at any node, the current entering must equal the current leaving.

Using Ohm’s Law to find current eliminates the need for Kirchhoff’s laws in simple circuits.

Calculation breakdown: total resistance in the loop is 10Ω, with 4 amps of current flowing.

Verification of Kirchhoff’s Voltage Law: summing voltage changes around the loop shows they equal zero.

Voltage rise across the battery: 40V; voltage drops across the resistors: 8V and 32V.

Confirmation that Kirchhoff's Voltage Law holds: 40 - 8 - 32 = 0.

Kirchhoff's laws become essential in complex circuits with multiple branches and voltage sources.

Kirchhoff’s laws help find currents and voltages in more complicated circuits with multiple loops or nodes.

Transcripts

Welcome to our lecture online here's our

first example of how to use kirov laws

notice in this particular case we have a

simple Loop a simple Loop circuit it is

a series circuit all the components are

connected in series meaning any two

components only sh share a single node

between them that is not shared by any

other Branch or any other component here

this is shared by these two components

this is shared by these two components

and this node is shared by these two

components and not by any others notice

I do have the circuit connected to

ground ground means that this part of

the circuit is equal to zero volt it's

simply a reference voltage we do that by

connecting it to a piece of metal or

something that can draw in a lot of

current and therefore we know or a lot

of charges I should say and therefore we

know that this will always be at zero

volts we're going to travel on the

around the loop in a clockwise direction

we sum up all the voltages around the

loop and they should add up to zero that

is that rule but what about the currents

can we use Kirk out rules on currents

well there's one note here let me put

little circle there there's another node

there there's another node there notice

that for any node the the current

entering the node must equal the current

leaving the node because there's just a

single current flowing through the

entire around the entire circuit around

the entire Loop so that doesn't help us

a lot we can use ohms law instead where

we can say that I is equal to V / R to

find the current in in the loop the

voltage is known it's 40 volts the

resistance we simply have to add up the

two resistors because they're in series

so in this case this is V / R1 + R2

which is equal to 40 Vols / 2 ohms Plus

8 ohms finally we can say that the

current in the circuit is equal to 40

Vol / 10 ohms which is equal to 4 amps

we have a 4 amp current flowing through

the circuit we didn't need we did not

need kov rules or kov laws to figure

that

out but what we should show is that when

we add up all the voltages going around

the loop they should add up to zero

Kirk's law says that the sum of all the

voltages around in Loop add up to zero

so let's go ahead and do that let's

start from this note right here let's go

around the loop in a clockwise Direction

first we go across the battery from the

negative end to the positive end that is

a 40 volt rise so 40 volts across the

battery now we travel across the

resistor in the same direction as the

current that means we add a voltage drop

that means it's a negative voltage rise

minus I the current times the resistor

R1 we travel across this resistor also

in the same direction as the current

again minus the current time R2 and that

should add up to zero because now we go

back to the same note where we started

from let's put in the currents and the

resistance to see if we got is correct

40 Vols minus the current which is the

current 4

amps times the resistor R1 of 2

ohms minus the current 4 amps times the

resistance of 8 ohms and that should add

up to zero notice here that the voltage

drop across the first resistor was 8

volts and the voltage dropped across the

second resistor was 32 volts and sure

enough 40 - 8 - 32 does add up to zero

and we've shown that kirkov law here

does work indeed we proved it by finding

the current using Ohm's law and then

using and applying kirov Second Law the

sum of all the voltages add up to zero

to show that it does inde work that way

you don't really need to use it for

something like this it's nice to show

that kirra's law does work but Kos laws

become extremely useful when the

circuits become much more complicated

when there's multiple branches multiple

voltage sources you definitely want to

use Kirk house rules to help you find

the currents and the voltages in the

circuit and across the branches that's

why we need Kirk house laws