For the resistor network shown, R1 = 4 Ω, R2 = 4 Ω and R3 = 5 Ω. Find the equivalent resistance from a to c. Give your answer in ohms. The image depicts a Wheatstone Bridge circuit, which is a fundamental electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.**Components and Labels:**- The circuit consists of four resistors: two labeled as $ R_1 $, one as $ R_2 $, and one as $ R_3 $.- Points $ a $, $ b $, and $ c $ are the junctions connecting these resistors.**Resistor Arrangement:**- Resistors $ R_1 $ are placed on the opposite sides of the bridge, creating the diagonal paths of the diamond shape.- Resistor $ R_2 $ connects the midpoint of the two diagonals.- Resistors $ R_3 $ are also placed symmetrically, completing the other sides of the diamond.**Functionality:**- The bridge is said to be "balanced" when the ratio of the resistances on one side of the bridge is equal to the ratio on the other side, i.e., $(R_1 / R_2) = (R_3 / R_1)$.- When balanced, no current flows through the bridge, meaning that unknown resistances can be calculated based on the known resistances.This circuit is commonly used in laboratories to precisely measure resistances, calibrate measuring instruments, and in various electronic applications.

Here, both the resistors R1 are in series, and the resistors R2 and R3 (between ab, and cb) are in…

Answered: For the resistor network shown, R1 = 4…

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)...

See similar textbooks

Related questions

Question

For the resistor network shown, R₁ = 4 Ω, R₂ = 4 Ω and R₃ = 5 Ω. Find the equivalent resistance from a to c. Give your answer in ohms.

The image depicts a Wheatstone Bridge circuit, which is a fundamental electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.

**Components and Labels:**
- The circuit consists of four resistors: two labeled as $ R_1 $, one as $ R_2 $, and one as $ R_3 $.
- Points $ a $, $ b $, and $ c $ are the junctions connecting these resistors.

**Resistor Arrangement:**
- Resistors $ R_1 $ are placed on the opposite sides of the bridge, creating the diagonal paths of the diamond shape.
- Resistor $ R_2 $ connects the midpoint of the two diagonals.
- Resistors $ R_3 $ are also placed symmetrically, completing the other sides of the diamond.

**Functionality:**
- The bridge is said to be "balanced" when the ratio of the resistances on one side of the bridge is equal to the ratio on the other side, i.e., $(R_1 / R_2) = (R_3 / R_1)$.
- When balanced, no current flows through the bridge, meaning that unknown resistances can be calculated based on the known resistances.

This circuit is commonly used in laboratories to precisely measure resistances, calibrate measuring instruments, and in various electronic applications.

Expert Solution

Step 1

Here, both the resistors R₁ are in series, and the resistors R₂ and R₃ (between ab, and cb) are in parallel. Determine the equivalent resistance of both the resistors R₁, and equivalent resistance of the resistors R₂ and R₃ (between ab, and cb), respectively, as follows.

$\begin{array}{rcl} R_{e q, 1} & = & R_{1} + R_{1} \\ = & 4 Ω + 4 Ω \\ = & 8 Ω \\ R_{e q, 2} & = & \frac{R_{2} R_{3}}{R_{2} + R_{3}} \\ = & \frac{(4 Ω) (5 Ω)}{4 Ω + 5 Ω} \\ = & 2.2222 Ω \end{array}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions