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1-14 How many independent equations can be obtained from the following circuit with Kirchhoff's Voltage Law? Explain your answer. ㅔㅏ V1 12V R1 3.3kQ www R2 3.3kQ W R3 3.3kQ

1-14 How many independent equations can be obtained from the following circuit with Kirchhoff's Voltage Law? Explain your answer. ㅔㅏ V1 12V R1 3.3kQ www R2 3.3kQ W R3 3.3kQ

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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**Question:** 1-14 How many independent equations can be obtained from the following circuit with Kirchhoff’s Voltage Law? Explain your answer. **Circuit Description:** - The circuit is a series-parallel combination with a voltage source and three resistors. - **Voltage Source (V1):** 12V - **Resistors:** - R1 = 3.3kΩ - R2 = 3.3kΩ - R3 = 3.3kΩ The circuit includes a 12V voltage source labeled V1, with three resistors (R1, R2, R3) each having a resistance of 3.3kΩ connected in parallel. **Explanation of Diagrams:** The diagram displays a straightforward parallel circuit structure: - The voltage source V1 is connected to three branches. - Each branch consists of one resistor (R1, R2, or R3). **Application of Kirchhoff's Voltage Law (KVL):** KVL states that the sum of all the voltages around any closed loop in a circuit is equal to zero. In the case of parallel circuits, the voltage across each component is the same as that across the source. For this circuit: - There is one loop involving V1, R1, R2, and R3. The voltage across each resistor in the loop equals the source voltage. - Therefore, only one independent KVL equation can be derived from this arrangement, reiterating the voltage drop: \[ V1 = V_{R1} = V_{R2} = V_{R3} = 12V \] The potential difference across each resistor equals the voltage of the source due to the parallel configuration. Hence, the single KVL equation reflects these conditions.
Transcribed Image Text:**Question:** 1-14 How many independent equations can be obtained from the following circuit with Kirchhoff’s Voltage Law? Explain your answer. **Circuit Description:** - The circuit is a series-parallel combination with a voltage source and three resistors. - **Voltage Source (V1):** 12V - **Resistors:** - R1 = 3.3kΩ - R2 = 3.3kΩ - R3 = 3.3kΩ The circuit includes a 12V voltage source labeled V1, with three resistors (R1, R2, R3) each having a resistance of 3.3kΩ connected in parallel. **Explanation of Diagrams:** The diagram displays a straightforward parallel circuit structure: - The voltage source V1 is connected to three branches. - Each branch consists of one resistor (R1, R2, or R3). **Application of Kirchhoff's Voltage Law (KVL):** KVL states that the sum of all the voltages around any closed loop in a circuit is equal to zero. In the case of parallel circuits, the voltage across each component is the same as that across the source. For this circuit: - There is one loop involving V1, R1, R2, and R3. The voltage across each resistor in the loop equals the source voltage. - Therefore, only one independent KVL equation can be derived from this arrangement, reiterating the voltage drop: \[ V1 = V_{R1} = V_{R2} = V_{R3} = 12V \] The potential difference across each resistor equals the voltage of the source due to the parallel configuration. Hence, the single KVL equation reflects these conditions.
### Kirchhoff's Voltage Law and the Conservation of Energy **Question:** 1-13 Describe Kirchhoff's Voltage Law. Explain how it relates to the principle of the conservation of energy. **Explanation:** Kirchhoff's Voltage Law (KVL) states that the sum of all electrical voltages around any closed network or loop is equal to zero. This law is fundamental in circuit analysis and is derived from the principle of conservation of energy. **Relation to the Conservation of Energy:** KVL reflects the conservation of energy in electrical circuits. When traversing a closed loop within a circuit, the total amount of electrical energy gained (through sources like batteries or generators) is equal to the total energy lost (through resistors or other components). Essentially, energy supplied is fully accounted for by energy dissipated or used within that loop, ensuring no net gain or loss of energy. This approach helps analyze complex electrical circuits systematically by setting up equations based on loop voltage sums, aiding in the calculation of unknown currents or voltages within the network.
Transcribed Image Text:### Kirchhoff's Voltage Law and the Conservation of Energy **Question:** 1-13 Describe Kirchhoff's Voltage Law. Explain how it relates to the principle of the conservation of energy. **Explanation:** Kirchhoff's Voltage Law (KVL) states that the sum of all electrical voltages around any closed network or loop is equal to zero. This law is fundamental in circuit analysis and is derived from the principle of conservation of energy. **Relation to the Conservation of Energy:** KVL reflects the conservation of energy in electrical circuits. When traversing a closed loop within a circuit, the total amount of electrical energy gained (through sources like batteries or generators) is equal to the total energy lost (through resistors or other components). Essentially, energy supplied is fully accounted for by energy dissipated or used within that loop, ensuring no net gain or loss of energy. This approach helps analyze complex electrical circuits systematically by setting up equations based on loop voltage sums, aiding in the calculation of unknown currents or voltages within the network.
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