Use Kirchhoff's junction rule and voltage/loop rule to find the current through each resistor in the following circuit: RAB = 10 2, RBC = 15 N, RAD = 6 2, RCD = 12 Q, RG = 4 2, and V. = 10 V. The Galvanometer G is a device with a small resistance that measures the current going through RG.
Use Kirchhoff's junction rule and voltage/loop rule to find the current through each resistor in the following circuit: RAB = 10 2, RBC = 15 N, RAD = 6 2, RCD = 12 Q, RG = 4 2, and V. = 10 V. The Galvanometer G is a device with a small resistance that measures the current going through RG.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
Apply the Junction Rule at B to determine the current going through RBC in terms of I1 and I3 .
![**Step 6: Solving Circuit Equations in a Wheatstone Bridge Network**
In this step, you are tasked with solving the circuit equations for the Wheatstone bridge configuration shown in the diagram. Your goal is to find the currents \( I_1, I_2, \) and \( I_3 \). Be sure to document your calculations in detail.
**Diagram Explanation:**
This diagram represents a Wheatstone bridge circuit, a common configuration used to measure unknown resistances. The circuit comprises four resistors \( R_{AB}, R_{BC}, R_{CD}, \) and \( R_{AD} \), arranged in a diamond shape. There is an additional galvanometer \( G \) between points B and D. Each resistor and the galvanometer contribute to the total resistance and potential difference in the circuit.
- **Points and Connections:**
- Points are labeled as A, B, C, D, F, H, and K.
- The battery voltage \( V_o \) is connected across points F and K.
- Arrows indicate the direction of current flow: \( I_1 \) flows from A to B, \( I_2 \) from A to D, and \( I_3 \) within the galvanometer from B to D.
**Kirchhoff's Loop Rule:**
Use Kirchhoff's loop rule to set up equations for each loop in the circuit:
1. **Loop ABGH:**
\[
V_{o} = I_1 \cdot R_{AB} + I_3 \cdot R_G
\]
2. **Loop BCDH:**
\[
I_3 \cdot R_G = I_3 \cdot R_{BC} + I_3 \cdot R_{CD}
\]
3. **Loop ADGH:**
\[
I_2 \cdot R_{AD} = I_2 \cdot R_{CD} + I_3 \cdot R_G
\]
Solve these equations simultaneously to find the values of \( I_1, I_2, \) and \( I_3 \).
Note: The bridge is balanced when the voltage across the galvanometer is zero, meaning \( I_3 = 0 \). Use this condition to simplify calculations when relevant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe112ce9-6954-4b71-9920-1f118927dc53%2Faeb22d8d-1944-4e27-b5f9-68460b7e8584%2Fu8b2gl5_processed.png&w=3840&q=75)
Transcribed Image Text:**Step 6: Solving Circuit Equations in a Wheatstone Bridge Network**
In this step, you are tasked with solving the circuit equations for the Wheatstone bridge configuration shown in the diagram. Your goal is to find the currents \( I_1, I_2, \) and \( I_3 \). Be sure to document your calculations in detail.
**Diagram Explanation:**
This diagram represents a Wheatstone bridge circuit, a common configuration used to measure unknown resistances. The circuit comprises four resistors \( R_{AB}, R_{BC}, R_{CD}, \) and \( R_{AD} \), arranged in a diamond shape. There is an additional galvanometer \( G \) between points B and D. Each resistor and the galvanometer contribute to the total resistance and potential difference in the circuit.
- **Points and Connections:**
- Points are labeled as A, B, C, D, F, H, and K.
- The battery voltage \( V_o \) is connected across points F and K.
- Arrows indicate the direction of current flow: \( I_1 \) flows from A to B, \( I_2 \) from A to D, and \( I_3 \) within the galvanometer from B to D.
**Kirchhoff's Loop Rule:**
Use Kirchhoff's loop rule to set up equations for each loop in the circuit:
1. **Loop ABGH:**
\[
V_{o} = I_1 \cdot R_{AB} + I_3 \cdot R_G
\]
2. **Loop BCDH:**
\[
I_3 \cdot R_G = I_3 \cdot R_{BC} + I_3 \cdot R_{CD}
\]
3. **Loop ADGH:**
\[
I_2 \cdot R_{AD} = I_2 \cdot R_{CD} + I_3 \cdot R_G
\]
Solve these equations simultaneously to find the values of \( I_1, I_2, \) and \( I_3 \).
Note: The bridge is balanced when the voltage across the galvanometer is zero, meaning \( I_3 = 0 \). Use this condition to simplify calculations when relevant.
Transcribed Image Text:**Kirchhoff's Circuit Analysis**
Use Kirchhoff’s junction rule and voltage/loop rule to find the current through each resistor in the following circuit: \( R_{AB} = 10 \, \Omega \), \( R_{BC} = 15 \, \Omega \), \( R_{AD} = 6 \, \Omega \), \( R_{CD} = 12 \, \Omega \), \( R_G = 4 \, \Omega \), and \( V_o = 10 \, V \).
The Galvanometer \( G \) is a device with a small resistance that measures the current going through \( R_G \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON