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What is the total reactance in Figure 13-2? 2.0 H 60 Hz 37.68 Ohms 753.6 Ohms 376.8 Ohms Figure 13 - 2 O 3,760.8 Ohms 2.0 H

What is the total reactance in Figure 13-2? 2.0 H 60 Hz 37.68 Ohms 753.6 Ohms 376.8 Ohms Figure 13 - 2 O 3,760.8 Ohms 2.0 H

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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### What is the total reactance in Figure 13-2? #### Diagram Explanation: The diagram shows an AC circuit containing two inductors, each with an inductance of 2.0 Henries, connected in series. The circuit is powered by an AC source with a frequency of 60 Hz. #### Total Reactance Calculation: The total reactance \( X_L \) of inductors in series is given by the formula: \[ X_L = 2\pi f L_{\text{total}} \] Where: - \( f = 60 \) Hz (frequency of the AC source) - \( L_{\text{total}} = L_1 + L_2 = 2.0 + 2.0 = 4.0 \) H (total inductance) Substituting these values: \[ X_L = 2\pi \times 60 \times 4.0 = 1508.8 \, \text{Ohms} \] This calculation does not match any choices directly, indicating a possible miscalculation in the example. For the purpose of the problem statement, the closest choice to the calculated value should be considered. ### Answer Choices: - 37.68 Ohms - 753.6 Ohms - **376.8 Ohms** (selected as the answer in the image) - 3,760.8 Ohms Note: The discrepancy suggests that the reactance might have been calculated for individual inductors or under different assumptions. Always verify calculations when learning circuit analysis.
Transcribed Image Text:### What is the total reactance in Figure 13-2? #### Diagram Explanation: The diagram shows an AC circuit containing two inductors, each with an inductance of 2.0 Henries, connected in series. The circuit is powered by an AC source with a frequency of 60 Hz. #### Total Reactance Calculation: The total reactance \( X_L \) of inductors in series is given by the formula: \[ X_L = 2\pi f L_{\text{total}} \] Where: - \( f = 60 \) Hz (frequency of the AC source) - \( L_{\text{total}} = L_1 + L_2 = 2.0 + 2.0 = 4.0 \) H (total inductance) Substituting these values: \[ X_L = 2\pi \times 60 \times 4.0 = 1508.8 \, \text{Ohms} \] This calculation does not match any choices directly, indicating a possible miscalculation in the example. For the purpose of the problem statement, the closest choice to the calculated value should be considered. ### Answer Choices: - 37.68 Ohms - 753.6 Ohms - **376.8 Ohms** (selected as the answer in the image) - 3,760.8 Ohms Note: The discrepancy suggests that the reactance might have been calculated for individual inductors or under different assumptions. Always verify calculations when learning circuit analysis.
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