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what is the total resistance

what is the total resistance

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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what is the total resistance

The image depicts an electrical circuit diagram, which includes a power source and multiple resistors connected in various combinations of series and parallel. ### Components of the Circuit: 1. **Voltage Source**: - A 5-volt DC power supply is shown, indicated by the symbol of a long line (positive) and a short line (negative). 2. **Resistors**: - **R1**: 1.0 kΩ (kilohms) resistor connected in series with the power source. - **R2**: 6.8 kΩ resistor connected in parallel with R3. - **R3**: 3.3 kΩ resistor connected in parallel with R2. - **R4**: 10 kΩ resistor connected in parallel with R5. - **R5**: 5.6 kΩ resistor connected in parallel with R4. ### Circuit Configuration: - **Series Connection**: - The resistor R1 is in series with the combined parallel connections of the other resistors. - **Parallel Connection**: - R2 and R3 are in a parallel configuration. - Similarly, R4 and R5 are connected in parallel. ### Analysis of the Circuit: - **Total Resistance**: - To find the total resistance of the circuit, first, calculate the equivalent resistance of the parallel connections: - Equivalent resistance of R2 and R3: \[ R_{eq1} = \frac{1}{\left( \frac{1}{R2} + \frac{1}{R3} \right)} \] - Equivalent resistance of R4 and R5: \[ R_{eq2} = \frac{1}{\left( \frac{1}{R4} + \frac{1}{R5} \right)} \] - Then, add the equivalent resistances to the series resistor R1: \[ R_{total} = R1 + R_{eq1} + R_{eq2} \] - **Current and Voltage Calculations**: - Use Ohm's Law (\( V = IR \)) to calculate the current across and the voltage drop in each component, once the total resistance is known. This circuit is a fundamental example used to demonstrate the calculations involved in analyzing the behavior of series-parallel resistor networks in an
Transcribed Image Text:The image depicts an electrical circuit diagram, which includes a power source and multiple resistors connected in various combinations of series and parallel. ### Components of the Circuit: 1. **Voltage Source**: - A 5-volt DC power supply is shown, indicated by the symbol of a long line (positive) and a short line (negative). 2. **Resistors**: - **R1**: 1.0 kΩ (kilohms) resistor connected in series with the power source. - **R2**: 6.8 kΩ resistor connected in parallel with R3. - **R3**: 3.3 kΩ resistor connected in parallel with R2. - **R4**: 10 kΩ resistor connected in parallel with R5. - **R5**: 5.6 kΩ resistor connected in parallel with R4. ### Circuit Configuration: - **Series Connection**: - The resistor R1 is in series with the combined parallel connections of the other resistors. - **Parallel Connection**: - R2 and R3 are in a parallel configuration. - Similarly, R4 and R5 are connected in parallel. ### Analysis of the Circuit: - **Total Resistance**: - To find the total resistance of the circuit, first, calculate the equivalent resistance of the parallel connections: - Equivalent resistance of R2 and R3: \[ R_{eq1} = \frac{1}{\left( \frac{1}{R2} + \frac{1}{R3} \right)} \] - Equivalent resistance of R4 and R5: \[ R_{eq2} = \frac{1}{\left( \frac{1}{R4} + \frac{1}{R5} \right)} \] - Then, add the equivalent resistances to the series resistor R1: \[ R_{total} = R1 + R_{eq1} + R_{eq2} \] - **Current and Voltage Calculations**: - Use Ohm's Law (\( V = IR \)) to calculate the current across and the voltage drop in each component, once the total resistance is known. This circuit is a fundamental example used to demonstrate the calculations involved in analyzing the behavior of series-parallel resistor networks in an
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