Network Theory 06 | Network Theorem (Part 02) | EE & ECE | GATE 2024 FastTrack Batch

GATE Wallah - EE, EC, CS & IN・2 minutes read

The lecture covers the Network Theorem, focusing on Thevenin and Norton cases, highlighting the calculation of Thevenin voltage and short-circuit current in networks with resistors and independent sources, alongside methods for determining equivalent resistance. Emphasizing the maximum power transfer theorem, the instructor encourages active student engagement and understanding of circuit analysis principles for successful application in electrical engineering.

Insights

  • The lecture focuses on the Network Theorem, particularly Thevenin and Norton cases, and emphasizes that understanding these concepts is essential for grasping the fundamentals of circuit analysis, especially after a missed class due to technical issues.
  • The instructor highlights the method for calculating equivalent resistance (RTA) in purely resistive networks by using series and parallel combinations, as well as concepts like equipotential and symmetry, which simplifies the analysis of the circuit.
  • When dealing with networks that include independent sources, the instructor explains the process of finding Thevenin voltage (BTH) and short-circuit current (ISC) by manipulating the circuit—opening terminals to find BTH and shorting them to determine ISC—illustrating the importance of these calculations in understanding circuit behavior.
  • The Maximum Power Transfer Theorem (MPTT) is introduced, explaining that maximum power is transferred when the load resistance equals the Thevenin resistance, and the instructor provides practical applications of this theorem in both DC and AC circuits while stressing the need for careful calculations.
  • The importance of efficiency in circuit analysis is discussed, with an emphasis on the 50% efficiency in DC circuits under MPTT conditions, and the instructor encourages students to engage actively with the material and prepare for more complex topics in future lectures.

Get key ideas from YouTube videos. It’s free

Recent questions

  • What is the maximum power transfer theorem?

    The maximum power transfer theorem (MPTT) states that to achieve maximum power transfer from a source to a load, the load resistance (RL) must equal the Thevenin resistance (RT) of the source circuit at the terminals where the load is connected. This principle applies to both direct current (DC) and alternating current (AC) circuits, although the specific calculations may differ based on the circuit type. To find the Thevenin equivalent resistance, one must first identify the open-circuit voltage (VTH) and then deactivate all independent sources in the circuit to calculate RT. Understanding this theorem is crucial for optimizing power delivery in electrical systems, as it ensures that the load receives the maximum possible power from the source, minimizing losses in the circuit.

  • How do you calculate equivalent resistance?

    To calculate the equivalent resistance (RTA) in a circuit, one must consider the configuration of the resistors involved. In purely resistive networks, RTA can be determined by using series and parallel combinations of resistors. For resistors in series, the total resistance is simply the sum of the individual resistances. In contrast, for resistors in parallel, the total resistance can be calculated using the formula 1/RTA = 1/R1 + 1/R2 + ... + 1/Rn. Additionally, when independent sources are present, it is essential to deactivate them appropriately—shorting independent voltage sources and opening independent current sources—to accurately find the equivalent resistance. This process is fundamental in circuit analysis, as it simplifies complex networks into manageable calculations.

  • What is Thevenin's theorem?

    Thevenin's theorem is a fundamental principle in circuit analysis that simplifies complex linear circuits into a simple equivalent circuit consisting of a single voltage source (Thevenin voltage, VTH) in series with a single resistance (Thevenin resistance, RT). To apply Thevenin's theorem, one first removes the load from the circuit and calculates the open-circuit voltage across the terminals, which becomes VTH. Next, the equivalent resistance is determined by deactivating all independent sources in the circuit. This theorem is particularly useful for analyzing circuits with multiple components, as it allows engineers to focus on the behavior of the load without needing to consider the entire network. Thevenin's theorem is widely used in electrical engineering for simplifying the analysis of circuits and understanding their behavior under varying load conditions.

  • How do you find short-circuit current?

    To find the short-circuit current (ISC) in a circuit, one must first short the terminals where the current is to be measured. This involves connecting a wire directly across the terminals, effectively creating a path with zero resistance. Once the terminals are shorted, the circuit can be analyzed to determine the current flowing through the short. The ISC can be calculated using Ohm's Law, where the current is derived from the known values of voltage and resistance in the circuit. It is crucial to understand the circuit configuration and apply the correct formulas to accurately calculate ISC. This value is significant in assessing the performance and safety of electrical systems, as it indicates the maximum current that can flow under fault conditions.

  • What is Kirchhoff's Voltage Law?

    Kirchhoff's Voltage Law (KVL) is a fundamental principle in electrical engineering that states that the sum of the electrical potential differences (voltages) around any closed loop in a circuit must equal zero. This law is based on the conservation of energy, indicating that the total energy supplied by sources in the loop is equal to the total energy consumed by the components within that loop. When applying KVL, one must account for the voltage rises (from sources) and voltage drops (across resistors and other components) in the circuit. This principle is essential for analyzing complex circuits, as it allows engineers to set up equations that describe the relationships between voltages in the circuit, facilitating the calculation of unknown values and ensuring the proper functioning of electrical systems.

Related videos

Summary

00:00

Understanding Thevenin and Norton Theorems

  • The lecture begins with an introduction, confirming it is Lecture Number 6, focusing on the topic of Network Theorem, specifically Thevenin and Norton cases, which will be covered in detail.
  • The instructor emphasizes that there are four cases to discuss regarding Thevenin and Norton, and notes that the previous class was missed due to a UPS issue, but they will proceed with the current lecture.
  • The first case involves a network with only resistors, where the Thevenin voltage (BTH) and short-circuit current (ISC) are both zero, as there are no independent sources present in the network.
  • To find the equivalent resistance (RTA) in a purely resistive network, the instructor advises using series and parallel combinations, as well as concepts of equipotential and symmetry, to simplify the calculations.
  • The example provided involves resistors of 2 ohms and 4 ohms in series and parallel configurations, leading to a calculated RTA of 4 ohms for the first case.
  • The second case introduces networks with both resistors and independent sources, where the first step is to calculate BTH by opening the terminals and analyzing the remaining circuit.
  • The instructor explains that when the terminals are opened, the current through the circuit becomes zero, leading to a BTH calculation of 8 volts based on the given circuit parameters.
  • The next step involves finding ISC by shorting the terminals, which allows for the calculation of the circuit current using the known values of voltage and resistance in the network.
  • The instructor provides a detailed explanation of how to set up the equations for ISC, emphasizing the importance of understanding the circuit configuration and applying the correct formulas.
  • Throughout the lecture, the instructor encourages student participation and understanding, using humor and relatable examples to clarify complex concepts in network theory.

15:19

Circuit Analysis and Current Calculations Explained

  • The initial calculation involves determining the value of ISC, which is derived from the equation 6 * 4 divided by 24/5, resulting in ISC being 24/5 or 4.8 milliamperes.
  • Further calculations show that dividing 4.8 by 3 yields 1.6 milliamperes, confirming the value of ISC as 1.6 mA.
  • When finding RTA in a network, it is crucial to identify independent voltage and current sources; independent voltage sources should be shorted, while independent current sources should be open-circuited.
  • It is emphasized that independent voltage sources can be shorted only when they are at zero volts, and independent current sources should never be shorted.
  • The process of deactivating sources is explained, where an independent voltage source is set to zero volts, allowing it to be represented as a short circuit, while an independent current source is represented as an open circuit.
  • A practical example is given with a circuit containing a 3kΩ resistor and a 2kΩ resistor, where the total resistance R is calculated as 5kΩ.
  • The discussion progresses to a more complex scenario involving both independent and dependent sources, with a specific circuit example featuring a 4V voltage source and resistances of 2Ω and 3Ω.
  • The first step in analyzing the circuit is to open the terminals to find the Thevenin equivalent voltage (BTH) and the short-circuit current (ISC).
  • The importance of applying nodal analysis is highlighted, with the expectation that students will calculate the current through the circuit accurately.
  • The final calculations involve using Kirchhoff's Voltage Law (KVL) to solve for the current in the circuit, ensuring that students understand the relationship between incoming and outgoing currents.

29:51

Understanding Voltage and Current in Circuits

  • The discussion begins with the relationship between voltage and current, emphasizing that if voltage rises, it will eventually drop, and the current is calculated as 1 - 1/4, leading to a voltage calculation of 4 volts.
  • The voltage is expressed as three times V1, and the total voltage is derived from the equation involving fractions, specifically 6/4 plus 3, resulting in a total of 4 volts.
  • The calculation of total voltage involves multiplying 2 by 3 to get 6, and then adding 3 to get a total of 11 volts, which is then divided by 2 to yield a final voltage of 8 volts.
  • The importance of understanding the first chapter of network theory is highlighted, as it serves as a foundational concept for grasping the entire subject matter.
  • The speaker emphasizes the significance of not neglecting the basics of Kirchhoff's Voltage Law (KVL) and encourages students to focus on understanding rather than rote memorization.
  • A short circuit scenario is introduced, where the speaker discusses the implications of short-circuiting a circuit with resistances of 1 ohm and 3 ohms, leading to a voltage of 4 volts.
  • The short-circuit current (ISC) is calculated, with the speaker explaining that if the voltage is zero, the current will also be zero, leading to a clear understanding of the circuit behavior.
  • Two methods for calculating equivalent resistance (RTA) are presented: Method One involves using short-circuit current, while Method Two, known as the test voltage and test current approach, is described as universally applicable across various cases.
  • The test voltage and test current method requires deactivating independent sources in the circuit, allowing for the calculation of outgoing current when a voltage source is applied.
  • The speaker stresses the importance of careful observation of terminal connections and current directions when applying these methods to ensure accurate calculations in network theory.

45:02

Understanding Voltage and Current in Circuits

  • The text discusses the concept of voltage and current in electrical circuits, emphasizing that the choice of voltage (e.g., 1 volt, 5000 volts, or 10 million volts) does not significantly affect the outcome of calculations related to current and resistance in the circuit.
  • It introduces the idea of "test voltage" and "test current" approaches, explaining that applying a specific voltage allows for the measurement of current in the circuit, which can be calculated using the formula: current (I) = voltage (V) / resistance (R).
  • The text mentions that if 1 volt is applied, the resulting current can be calculated as 1/4 ampere, indicating a direct relationship between voltage and current based on Ohm's Law.
  • It highlights the importance of calculating the total current in a circuit, stating that the sum of incoming and outgoing currents must equal zero, which is a fundamental principle in circuit analysis.
  • The author emphasizes the need to calculate the equivalent resistance (RTA) in circuits with dependent sources, suggesting that if there is no independent source, both the Thevenin voltage (BTH) and the short-circuit current (ISC) will be zero.
  • A specific example is provided where a circuit with a resistance of 2 ohms and a dependent source is analyzed, guiding the reader through the steps to find RTA and ISC.
  • The text advises using the test voltage and test current approaches as methods to analyze circuits without independent sources, reinforcing that these methods act as independent sources themselves.
  • It warns against overconfidence in circuit analysis, stressing the importance of careful calculations and understanding the principles behind the methods used.
  • The author encourages students to practice calculations and understand the relationships between voltage, current, and resistance to prepare for examinations effectively.
  • The text concludes with a reminder that understanding these concepts is crucial for success in electrical engineering and circuit analysis, urging students to engage actively with the material.

59:43

Understanding Maximum Power Transfer Theorem

  • To conduct a test, apply a test voltage of ±1 volt and measure the current (i) at terminal A, while noting the terminal resistance at terminal B, which is specified as 2 ohms, 1 ohm, and 0.5 ohms in different scenarios.
  • If the applied voltage is 1 volt, the resulting current (i) can be calculated using the formula i = 1 / R, where R is the resistance; for a resistance of 2 ohms, the current will be 0.5 amperes.
  • The relationship between voltage and current indicates that if both terminals show 1 volt, the voltage difference across them will be 0 volts, resulting in 0 amperes of current.
  • The maximum power transfer theorem (MPTT) states that to achieve maximum power transfer, the load resistance (RL) must equal the Thevenin resistance (RT) at the terminals where the load is connected.
  • To find the Thevenin equivalent resistance (RT) at the terminals, first identify the open-circuit voltage (VTH) and then calculate RT by deactivating all independent sources in the circuit.
  • When calculating load power, use the formula P = I² * R, where I is the current through the load and R is the load resistance; this power is variable as long as RL remains a variable.
  • The condition for maximum power transfer is established by differentiating the power equation with respect to RL and setting the derivative equal to zero, which leads to the conclusion that RL must equal RT.
  • The MPTT is applicable in both DC and AC circuits, but the specific calculations and conditions may vary based on the circuit type.
  • It is crucial to remember that the Thevenin equivalent circuit parameters (VTH and RT) remain constant unless changes are made to the circuit elements, particularly the load.
  • The key points for applying the MPTT include ensuring that RL is treated as a variable, confirming that RL equals RT for maximum power, and understanding the relationship between the load and the circuit's Thevenin equivalent.

01:17:24

Understanding Power Transfer in Circuits

  • The discussion begins with a focus on calculating the value of a PTT card, emphasizing the need to understand the relationship between variables such as T and R, and how to apply the voltage division rule when both values are equal, indicating that higher voltage leads to higher output.
  • It is highlighted that the source power is crucial, with a specific inquiry into how much current is flowing into the source, and the importance of determining the power transfer under MPTT (Maximum Power Transfer Theorem) conditions, which requires calculating the power supplied to the load and the losses incurred.
  • The text mentions a specific power loss of 8H in the source circuit, instructing to calculate this loss using the formula involving the square of the voltage divided by the resistance, emphasizing the need to understand how much power is being lost in the circuit.
  • Efficiency is discussed in relation to output power, with a specific focus on the maximum power transfer at 50, indicating that the power loss in RTA (Resistance to Load) is significant, and the source must provide double the power to compensate for losses.
  • The importance of efficiency in DC circuits is stressed, stating that efficiency is always at 50% under MPTT conditions, while in AC circuits, efficiency can vary and may not always be optimal, highlighting the need for careful consideration of efficiency versus power output.
  • The session concludes with a plan to discuss the Network Theorem in the next meeting, encouraging students to prepare questions and emphasizing the importance of understanding complex concepts like the chaos theorem and black box problems in circuit analysis.
Channel avatarChannel avatarChannel avatarChannel avatarChannel avatar

Try it yourself — It’s free.