what is the total resistance
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F737d345c-09bc-4ad4-85fb-0d2430d87582%2Fbf8f5a32-0f59-4cf7-b6c2-950d2c6e4182%2Ff0xejoo_processed.jpeg&w=3840&q=75)
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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