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10. All of the resistors and batteries are identical in the circuits shown. Rank the total resistance that the circuits present to the battery. C D F OR All the same All Cannot determine Greatest Least zero W-

10. All of the resistors and batteries are identical in the circuits shown. Rank the total resistance that the circuits present to the battery. C D F OR All the same All Cannot determine Greatest Least zero W-

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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**Problem Description:** 10. All of the resistors and batteries are identical in the circuits shown. Rank the total resistance that the circuits present to the battery. **Diagrams:** - **Circuit A**: Two resistors in series. - **Circuit B**: Two resistors in parallel. - **Circuit C**: One resistor in series with two parallel resistors. - **Circuit D**: Three resistors in parallel. - **Circuit E**: Two resistors in series, parallel to a single resistor. - **Circuit F**: Three resistors in series. There is a bar with positions labeled "Greatest 1 2 3 4 5 6 Least". There are also options "All the same", "All zero", and "Cannot determine". **Explanation:** To rank the total resistance presented to the battery by each circuit: - Calculate the equivalent resistance for series and parallel combinations for each circuit diagram. **Steps:** 1. **Series combination**: Resistance adds up directly (R_total = R1 + R2 + ... + Rn). 2. **Parallel combination**: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances (1/R_total = 1/R1 + 1/R2 + ... + 1/Rn). **Ranking Process:** 1. **Circuit A**: Total Resistance, \( R_A = R + R = 2R \). 2. **Circuit B**: Total Resistance, \( 1/R_B = 1/R + 1/R = 2/R \), thus \( R_B = R/2 \). 3. **Circuit C**: Total Resistance, \( R_C = R + (1/(1/R + 1/R)) = R + R/2 = 1.5R \). 4. **Circuit D**: Total Resistance, \( 1/R_D = 1/R + 1/R + 1/R = 3/R \), thus \( R_D = R/3 \). 5. **Circuit E**: Total Resistance, \( 1/R_E = 1/(R + R) + 1/R = 1/2R + 1/R = 1/2R + 2/2R = 3/2R \), thus \( R_E = 2R/3 \). 6. **Circuit F**: Total Resistance,
Transcribed Image Text:**Problem Description:** 10. All of the resistors and batteries are identical in the circuits shown. Rank the total resistance that the circuits present to the battery. **Diagrams:** - **Circuit A**: Two resistors in series. - **Circuit B**: Two resistors in parallel. - **Circuit C**: One resistor in series with two parallel resistors. - **Circuit D**: Three resistors in parallel. - **Circuit E**: Two resistors in series, parallel to a single resistor. - **Circuit F**: Three resistors in series. There is a bar with positions labeled "Greatest 1 2 3 4 5 6 Least". There are also options "All the same", "All zero", and "Cannot determine". **Explanation:** To rank the total resistance presented to the battery by each circuit: - Calculate the equivalent resistance for series and parallel combinations for each circuit diagram. **Steps:** 1. **Series combination**: Resistance adds up directly (R_total = R1 + R2 + ... + Rn). 2. **Parallel combination**: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances (1/R_total = 1/R1 + 1/R2 + ... + 1/Rn). **Ranking Process:** 1. **Circuit A**: Total Resistance, \( R_A = R + R = 2R \). 2. **Circuit B**: Total Resistance, \( 1/R_B = 1/R + 1/R = 2/R \), thus \( R_B = R/2 \). 3. **Circuit C**: Total Resistance, \( R_C = R + (1/(1/R + 1/R)) = R + R/2 = 1.5R \). 4. **Circuit D**: Total Resistance, \( 1/R_D = 1/R + 1/R + 1/R = 3/R \), thus \( R_D = R/3 \). 5. **Circuit E**: Total Resistance, \( 1/R_E = 1/(R + R) + 1/R = 1/2R + 1/R = 1/2R + 2/2R = 3/2R \), thus \( R_E = 2R/3 \). 6. **Circuit F**: Total Resistance,
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