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Sample Problem continued with solution process Step 1: Drawing a circuit diagram and labeling the unknowns. All told there are 5 elements, 4 resistors and 1 voltage source. For resistors I intentionally label the currents going from + to -. That way, I can write V =| R. If I labeled the current through a resistor from – to + as I, then I have to write the equation by Ohm's law as V = -I R. For convenience I label the current i, through the voltage source from – to +. (There is no Ohm's law for a source to follow. Do not try to have a |1A 10 N + + V, 2 20Ω 4 I then examine the circuit. I see that this is a obvious consequence of the labeling: İ3 = i,= i, All are current going through one path with the same direction as I labeled. If I had labeled one in the opposite direction, I just had to put in a minus sign. resistance in a source. What is a source? A voltage source is to guarantee the voltage drop from its + to its – a fixed voltage V. I denote four points in the circuit with numbers encircled. They help me apply KVL and KCL.

Sample Problem continued with solution process Step 1: Drawing a circuit diagram and labeling the unknowns. All told there are 5 elements, 4 resistors and 1 voltage source. For resistors I intentionally label the currents going from + to -. That way, I can write V =| R. If I labeled the current through a resistor from – to + as I, then I have to write the equation by Ohm's law as V = -I R. For convenience I label the current i, through the voltage source from – to +. (There is no Ohm's law for a source to follow. Do not try to have a |1A 10 N + + V, 2 20Ω 4 I then examine the circuit. I see that this is a obvious consequence of the labeling: İ3 = i,= i, All are current going through one path with the same direction as I labeled. If I had labeled one in the opposite direction, I just had to put in a minus sign. resistance in a source. What is a source? A voltage source is to guarantee the voltage drop from its + to its – a fixed voltage V. I denote four points in the circuit with numbers encircled. They help me apply KVL and KCL.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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# Sample Problem continued with solution process ## Step 1: Drawing a circuit diagram and labeling the unknowns. ### Circuit Diagram Description: - The circuit contains: - 5 elements: 4 resistors and 1 voltage source. - Nodes labeled 1, 2, 3, and 4. - A 10 Ω resistor with voltage \( V_1 \) and current \( i_1 \). - A 2 Ω resistor with voltage \( V_2 \) and current \( i_2 \). - A 20 Ω resistor with voltage \( V_3 \) and current \( i_3 \). - A 5 Ω resistor with voltage \( V_4 \) and current \( i_4 \), with a fixed 1 A current. - Voltage source \( V_s \) with current \( i_s \). ### Key Insights: - **Labeling:** - Resistive currents are labeled from \( + \) to \( - \) (V = I R). - Current \( i_s \) is labeled through the voltage source from \( - \) to \( + \). - **Observations:** - \( i_3 = i_s = i_1 \), indicating current through one path in the same direction as labeled. ### Notes: - **Ohm’s Law:** For current through resistors, use \( V = I R \). - **Voltage Source:** No resistance. Ensures fixed voltage \( V_s \) across its terminals. - **Reference Points:** Four points help apply Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL).
Transcribed Image Text:# Sample Problem continued with solution process ## Step 1: Drawing a circuit diagram and labeling the unknowns. ### Circuit Diagram Description: - The circuit contains: - 5 elements: 4 resistors and 1 voltage source. - Nodes labeled 1, 2, 3, and 4. - A 10 Ω resistor with voltage \( V_1 \) and current \( i_1 \). - A 2 Ω resistor with voltage \( V_2 \) and current \( i_2 \). - A 20 Ω resistor with voltage \( V_3 \) and current \( i_3 \). - A 5 Ω resistor with voltage \( V_4 \) and current \( i_4 \), with a fixed 1 A current. - Voltage source \( V_s \) with current \( i_s \). ### Key Insights: - **Labeling:** - Resistive currents are labeled from \( + \) to \( - \) (V = I R). - Current \( i_s \) is labeled through the voltage source from \( - \) to \( + \). - **Observations:** - \( i_3 = i_s = i_1 \), indicating current through one path in the same direction as labeled. ### Notes: - **Ohm’s Law:** For current through resistors, use \( V = I R \). - **Voltage Source:** No resistance. Ensures fixed voltage \( V_s \) across its terminals. - **Reference Points:** Four points help apply Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL).
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