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A) State Kirchhoff's Voltage Law (KVL). B) Determine the loop currents (11 and 12) using mesh-current analysis technique. Given that Vs=10V Is=2A, R1=522, R2=292. V₂ R₁ I₁ R₂ www Is 1₂

A) State Kirchhoff's Voltage Law (KVL). B) Determine the loop currents (11 and 12) using mesh-current analysis technique. Given that Vs=10V Is=2A, R1=522, R2=292. V₂ R₁ I₁ R₂ www Is 1₂

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Kirchhoff's Voltage Law and Mesh-Current Analysis **A) State Kirchhoff’s Voltage Law (KVL).** Kirchhoff's Voltage Law (KVL) states that the sum of all electrical potential differences (voltages) around any closed network (loop) is zero. Mathematically, it can be represented as: \[ \sum_{k=1}^{n} V_k = 0 \] This implies that the total amount of voltage around a closed loop must equal zero, considering both the voltage sources and drops within the loop. **B) Determine the loop currents (I1 and I2) using the mesh-current analysis technique. Given that Vs=10V, Is=2A, R1=5Ω, R2=2Ω.** #### Circuit Diagram Description: The circuit consists of two mesh loops with shared components. - **Loop 1** includes: - Voltage source \( V_s \) - Resistor \( R_1 \) - **Loop 2** includes: - Resistor \( R_2 \) - Current source \( I_s \) The loops are designated as: - Loop 1: Counterclockwise with current \( I_1 \) - Loop 2: Counterclockwise with current \( I_2 \) #### Given Values: - \( V_s = 10V \) - \( I_s = 2A \) - \( R_1 = 5Ω \) - \( R_2 = 2Ω \) #### Mesh-Current Analysis: To find currents \( I_1 \) and \( I_2 \), we apply KVL to each loop. **For Loop 1:** \[ V_s - I_1 R_1 - I_s R_1 = 0 \] \[ 10V - 5Ω(I_1) - 2A \cdot 5Ω = 0 \] \[ 10V - 5ΩI_1 - 10V = 0 \] \[ - 5ΩI_1 = 0 \] \[ I_1 = 0A \] **For Loop 2:** Since the second loop includes a current source, the loop current \( I_2 \) is directly influenced by the current source \( I_s \): \[ I_2 = I_s \] \[ I_2 = 2A \] #### Results
Transcribed Image Text:### Kirchhoff's Voltage Law and Mesh-Current Analysis **A) State Kirchhoff’s Voltage Law (KVL).** Kirchhoff's Voltage Law (KVL) states that the sum of all electrical potential differences (voltages) around any closed network (loop) is zero. Mathematically, it can be represented as: \[ \sum_{k=1}^{n} V_k = 0 \] This implies that the total amount of voltage around a closed loop must equal zero, considering both the voltage sources and drops within the loop. **B) Determine the loop currents (I1 and I2) using the mesh-current analysis technique. Given that Vs=10V, Is=2A, R1=5Ω, R2=2Ω.** #### Circuit Diagram Description: The circuit consists of two mesh loops with shared components. - **Loop 1** includes: - Voltage source \( V_s \) - Resistor \( R_1 \) - **Loop 2** includes: - Resistor \( R_2 \) - Current source \( I_s \) The loops are designated as: - Loop 1: Counterclockwise with current \( I_1 \) - Loop 2: Counterclockwise with current \( I_2 \) #### Given Values: - \( V_s = 10V \) - \( I_s = 2A \) - \( R_1 = 5Ω \) - \( R_2 = 2Ω \) #### Mesh-Current Analysis: To find currents \( I_1 \) and \( I_2 \), we apply KVL to each loop. **For Loop 1:** \[ V_s - I_1 R_1 - I_s R_1 = 0 \] \[ 10V - 5Ω(I_1) - 2A \cdot 5Ω = 0 \] \[ 10V - 5ΩI_1 - 10V = 0 \] \[ - 5ΩI_1 = 0 \] \[ I_1 = 0A \] **For Loop 2:** Since the second loop includes a current source, the loop current \( I_2 \) is directly influenced by the current source \( I_s \): \[ I_2 = I_s \] \[ I_2 = 2A \] #### Results
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