Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![### Electrical Circuit Analysis
**Problem Statement:**
2. For the circuit shown below, calculate:
a. The total resistance
b. The total current
c. The power dissipated in each resistor
**Diagram Description:**
The circuit is a simple parallel circuit consisting of a voltage source and three resistors.
- **Voltage Source (Vs):** 45V
- **Resistor R1:** 60kΩ
- **Resistor R2:** 15kΩ
- **Resistor R3:** 60kΩ
**Steps to Solve:**
**a. Calculate the Total Resistance (R_total):**
For resistors in parallel, the total resistance can be calculated using the formula:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
Plug in the values:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{60k\Omega} + \frac{1}{15k\Omega} + \frac{1}{60k\Omega}
\]
**b. Calculate the Total Current (I_total):**
Ohm's Law (V = IR) is used to find the total current. Once the total resistance is found from part (a), use:
\[
I_{\text{total}} = \frac{V}{R_{\text{total}}}
\]
**c. Calculate the Power Dissipated in Each Resistor:**
The power dissipated in a resistor can be calculated using the formula:
\[
P = I^2 \times R
\]
However, when dealing with parallel circuits, you can also use:
\[
P = \frac{V^2}{R}
\]
Calculate for each resistor:
- **Power in R1:**
\[
P_1 = \frac{(45V)^2}{60k\Omega}
\]
- **Power in R2:**
\[
P_2 = \frac{(45V)^2}{15k\Omega}
\]
- **Power in R3:**
\[
P_3 = \frac{(45V)^2}{60k\Omega}
\]
This completes the analysis of the given circuit.](https://content.bartleby.com/qna-images/question/f7186c19-f484-472d-921d-33d7fb24a522/eced490b-47e3-4837-826d-16bde6acc3b6/17bccdj_processed.png)
Transcribed Image Text:### Electrical Circuit Analysis
**Problem Statement:**
2. For the circuit shown below, calculate:
a. The total resistance
b. The total current
c. The power dissipated in each resistor
**Diagram Description:**
The circuit is a simple parallel circuit consisting of a voltage source and three resistors.
- **Voltage Source (Vs):** 45V
- **Resistor R1:** 60kΩ
- **Resistor R2:** 15kΩ
- **Resistor R3:** 60kΩ
**Steps to Solve:**
**a. Calculate the Total Resistance (R_total):**
For resistors in parallel, the total resistance can be calculated using the formula:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
Plug in the values:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{60k\Omega} + \frac{1}{15k\Omega} + \frac{1}{60k\Omega}
\]
**b. Calculate the Total Current (I_total):**
Ohm's Law (V = IR) is used to find the total current. Once the total resistance is found from part (a), use:
\[
I_{\text{total}} = \frac{V}{R_{\text{total}}}
\]
**c. Calculate the Power Dissipated in Each Resistor:**
The power dissipated in a resistor can be calculated using the formula:
\[
P = I^2 \times R
\]
However, when dealing with parallel circuits, you can also use:
\[
P = \frac{V^2}{R}
\]
Calculate for each resistor:
- **Power in R1:**
\[
P_1 = \frac{(45V)^2}{60k\Omega}
\]
- **Power in R2:**
\[
P_2 = \frac{(45V)^2}{15k\Omega}
\]
- **Power in R3:**
\[
P_3 = \frac{(45V)^2}{60k\Omega}
\]
This completes the analysis of the given circuit.
Expert Solution
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