For the circuit below using Kirchhoff's Voltage Law, determine the value of VRI and VR2: (Provide your calculations and reasoning for your answer.)
For the circuit below using Kirchhoff's Voltage Law, determine the value of VRI and VR2: (Provide your calculations and reasoning for your answer.)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![## Problem Statement
For the circuit below, using Kirchhoff’s Voltage Law, determine the value of \( V_{R1} \) and \( V_{R2} \). Provide your calculations and reasoning for your answer.
### Circuit Description
The circuit consists of:
- Three voltage sources:
- \( V_{S1} = 1.5 \, V \)
- \( V_{S2} = 12.5 \, V \)
- \( V_{S3} = 2.4 \, V \)
- Three resistors with the following voltage drops:
- \( V_{R3} = 8.3 \, V \)
- Unknown values for \( V_{R1} \) and \( V_{R2} \) which need to be determined.
### Circuit Layout
- \( V_{S1} \) is placed in series at the beginning of the loop.
- \( V_{R3} \) is in series with \( V_{S1} \).
- \( V_{S2} \) follows, in series with \( V_{R1} \).
- In the same branch, \( V_{S3} \) is paired with \( V_{R2} \).
### Calculations and Analysis
To solve for \( V_{R1} \) and \( V_{R2} \), apply Kirchhoff’s Voltage Law (KVL):
1. **KVL Equation**:
- The sum of the electromotive forces (emf) is equal to the sum of the potential drops (resistances) in a closed loop.
- Loop equation:
\[
V_{S1} + V_{S2} + V_{S3} = V_{R1} + V_{R2} + V_{R3}
\]
- Substitute the known values:
\[
1.5 + 12.5 + 2.4 = V_{R1} + V_{R2} + 8.3
\]
- Simplify:
\[
16.4 = V_{R1} + V_{R2} + 8.3
\]
- Solve for the unknowns:
\[
V_{R1} + V_{R2} = 16.4 - 8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3c22a28-8e9a-42a1-ac26-114f2e495bee%2F56c299fb-3b2c-4d29-bd59-ea4d9b0f835d%2Fkqybfh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Statement
For the circuit below, using Kirchhoff’s Voltage Law, determine the value of \( V_{R1} \) and \( V_{R2} \). Provide your calculations and reasoning for your answer.
### Circuit Description
The circuit consists of:
- Three voltage sources:
- \( V_{S1} = 1.5 \, V \)
- \( V_{S2} = 12.5 \, V \)
- \( V_{S3} = 2.4 \, V \)
- Three resistors with the following voltage drops:
- \( V_{R3} = 8.3 \, V \)
- Unknown values for \( V_{R1} \) and \( V_{R2} \) which need to be determined.
### Circuit Layout
- \( V_{S1} \) is placed in series at the beginning of the loop.
- \( V_{R3} \) is in series with \( V_{S1} \).
- \( V_{S2} \) follows, in series with \( V_{R1} \).
- In the same branch, \( V_{S3} \) is paired with \( V_{R2} \).
### Calculations and Analysis
To solve for \( V_{R1} \) and \( V_{R2} \), apply Kirchhoff’s Voltage Law (KVL):
1. **KVL Equation**:
- The sum of the electromotive forces (emf) is equal to the sum of the potential drops (resistances) in a closed loop.
- Loop equation:
\[
V_{S1} + V_{S2} + V_{S3} = V_{R1} + V_{R2} + V_{R3}
\]
- Substitute the known values:
\[
1.5 + 12.5 + 2.4 = V_{R1} + V_{R2} + 8.3
\]
- Simplify:
\[
16.4 = V_{R1} + V_{R2} + 8.3
\]
- Solve for the unknowns:
\[
V_{R1} + V_{R2} = 16.4 - 8.
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