# 17 Lecture

## Examples of Loop Analysis

Loop analysis, also known as Kirchhoff’s Voltage Law (KVL), is a powerful tool in circuit theory that allows engineers and technicians to analyze and solve complex electrical circuits.

## Important Mcq's Midterm & Finalterm Prepration Past papers included

In the circuit shown below, what is the current flowing through the 6-ohm resistor?

10 V

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|    4 ohm    |

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6 ohm

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a) 0.25 A

b) 0.5 A

c) 1 A

d) 2 A

In the circuit shown below, what is the voltage across the 2-ohm resistor?

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3V

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|    4 ohm    |

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2 ohm

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a) 0.5 V

b) 1 V

c) 1.5 V

d) 2 V

In the circuit shown below, what is the voltage across the 5-ohm resistor?

lua

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5V

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|    3 ohm    |

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5 ohm

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a) 1 V

b) 2 V

c) 3 V

d) 4 V

In the circuit shown below, what is the current flowing through the 10-ohm resistor?

lua

Copy code

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2V

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|    6 ohm    |

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10 ohm

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a) 0.1 A

b) 0.2 A

c) 0.3 A

d) 0.4 A

In the circuit shown below, what is the voltage across the 4-ohm resistor?

lua

10V

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|    3 ohm    |

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4 ohm

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a) 2 V

b) 4 V

c) 6 V

d) 8 V

In the circuit shown below, what is the current flowing through the 2-ohm resistor?

lua

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6V

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|    3 ohm    |

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2 ohm

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a) 1 A

b) 2 A

c) 3 A

d) 4 A

In the circuit shown below, what is the voltage across the 6-ohm resistor?

markdown

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9

## Subjective Short Notes Midterm & Finalterm Prepration Past papers included

What are coupling equations?

A: Coupling equations are a set of mathematical expressions used to describe the interaction between different modes in a system.

In which fields are coupling equations commonly used?

A: Coupling equations are commonly used in fields such as optics, electromagnetics, and acoustics.

What is the basic idea behind coupling equations?

A: The basic idea behind coupling equations is that when two modes are present in a system, they interact with each other, which leads to a transfer of energy between the modes.

How are coupling equations used to describe the behavior of resonators in a waveguide?

A: In a coupled resonator optical waveguide (CROW), the interaction between different resonators leads to the formation of photonic bands, which can be described using a set of coupling equations.

How are coupling equations used to describe the behavior of antennas in electromagnetics?

A: In a coupled microstrip antenna array, the interaction between the individual antenna elements leads to the formation of a directional radiation pattern, which can be described using a set of coupling equations.

What is the most common form of coupling equations?

A: The most common form of coupling equations is the coupled mode theory (CMT).

How does CMT assume the coupling between modes in a system?

A: CMT assumes that the modes in a system are weakly coupled, and that the coupling can be described using a linear set of equations.

What is the basic approach of CMT to solve the coupling equations?

A: The basic approach of CMT is to write down a set of equations that describe the behavior of each individual mode in the system, and then to introduce a coupling term that describes the interaction between the different modes.

How are numerical methods used to solve the coupling equations?

A: Numerical methods, such as finite element analysis or the boundary element method, can be used to solve the coupling equations.

What is the benefit of using coupling equations to describe complex systems?

A: Coupling equations provide a powerful tool for describing the behavior of complex systems that involve multiple modes, and can be used to predict the behavior of these systems with a high degree of accuracy.

### Examples of Loop Analysis

Loop analysis, also known as Kirchhoff’s Voltage Law (KVL), is a powerful tool in circuit theory that allows engineers and technicians to analyze and solve complex electrical circuits. Loop analysis is a method used to determine the currents and voltages in a circuit by analyzing the loops of the circuit. In this article, we will explore some examples of loop analysis in circuit theory.

### Example 1: Simple Circuit

Let's consider the following circuit with a single loop and a single voltage source. We need to determine the current flowing through the resistor. Simple Circuit Using Kirchhoff’s Voltage Law, we can write: V = IR where V is the voltage of the source, I is the current flowing through the resistor, and R is the resistance of the resistor. Rearranging this equation, we get: I = V / R Substituting the values, we get: I = 10 / 1000 = 0.01 A Therefore, the current flowing through the resistor is 0.01 A.

### Example 2: Circuit with Multiple Loops

Let's consider the following circuit with two loops and two voltage sources. We need to determine the current flowing through the 2 ? resistor. Circuit with Multiple Loops We can use Kirchhoff’s Voltage Law to analyze this circuit. Let’s define the currents flowing through the loops as I1 and I2, respectively. Applying Kirchhoff’s Voltage Law in Loop 1, we get: -10 + 4I1 - 2I2 = 0 Applying Kirchhoff’s Voltage Law in Loop 2, we get: -6 + 2I2 - 4I1 - 2I2 = 0 Simplifying the second equation, we get: -6 - 2I1 = 0 Solving the equations, we get: I1 = 1 A I2 = 3 A Therefore, the current flowing through the 2 ? resistor is 2 A. Example 3: Circuit with Dependent Sources Let's consider the following circuit with a dependent current source and two loops. We need to determine the voltage across the 4 ? resistor. Circuit with Dependent Sources We can use Kirchhoff’s Voltage Law to analyze this circuit. Let’s define the currents flowing through the loops as I1 and I2, respectively. Applying Kirchhoff’s Voltage Law in Loop 1, we get: -10 + 8I1 - 2I2 = 0 Applying Kirchhoff’s Voltage Law in Loop 2, we get: -2 + 2I2 - 4I1 = 0 Substituting the value of I2 from the first equation into the second equation, we get: -2 + 2(10 - 4I1) - 4I1 = 0 Simplifying the equation, we get: I1 = 1.5 A Using Kirchhoff’s Voltage Law in Loop 1, we can calculate the voltage across the 4 ? resistor as: V = 4I1 = 4 x 1.5 = 6 V Therefore, the voltage across the 4 ? resistor is 6 V. Example 4: Circuit with Nonlinear Elements Let's consider the following circuit with a diode and two loops. We need to determine the voltage across the diode.