**Problem Statement:**For a balanced Wheatstone bridge (i.e., when the null condition is met, \( E_0 = 0 \)), with the given resistances \( R_2 = 5 \text{ kOhm} \), \( R_3 = 27 \text{ kOhm} \), and \( R_4 = 9 \text{ kOhm} \), find the value of \( R_1 \).**Diagram Explanation:**The diagram is a schematic representation of a Wheatstone bridge circuit. The bridge is composed of four resistors:- \( R_1 \) is connected between points \( A \) and \( E_C \).- \( R_2 = 5 \text{ kOhm} \) is connected between points \( B \) and \( E_C \).- \( R_3 = 27 \text{ kOhm} \) is connected between points \( A \) and \( E_D \).- \( R_4 = 9 \text{ kOhm} \) is connected between points \( B \) and \( E_D \).The bridge is powered by a voltage source \( E_s \) across points \( E_C \) and \( B \).In the balanced condition, the potential difference \( E_0 \) between the junction points \( E_C \) and \( E_D \) is zero.**Solution:**For a Wheatstone bridge to be balanced, the following condition must be satisfied:\[\frac{R_1}{R_2} = \frac{R_3}{R_4}\]Substitute the known values:\[\frac{R_1}{5 \text{ kOhm}} = \frac{27 \text{ kOhm}}{9 \text{ kOhm}}\]Solving for \( R_1 \):\[R_1 = \frac{5 \times 27}{9} \text{ kOhm}\]Simplify to find:\[R_1 = 15 \text{ kOhm}\]Thus, the value of \( R_1 \) is \( 15 \text{ kOhm} \).

Given: R2=5 kΩ, R3=27 kΩ, R4=9 kΩ Null condition, Eo=0.

Answered: 4) For a balanced Wheatstone bridge…

4) For a balanced Wheatstone bridge (ie. when null condition is met, Eo = 0) R2= 5k Ohm, R3= 27 k Ohm, R4 = 9 kOhm, find the value of R1. A R1 R3 Es Eo Ec in R4 R2 B

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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)...

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Question

**Problem Statement:**

For a balanced Wheatstone bridge (i.e., when the null condition is met, \( E_0 = 0 \)), with the given resistances \( R_2 = 5 \text{ kOhm} \), \( R_3 = 27 \text{ kOhm} \), and \( R_4 = 9 \text{ kOhm} \), find the value of \( R_1 \).

**Diagram Explanation:**

The diagram is a schematic representation of a Wheatstone bridge circuit. The bridge is composed of four resistors:

- \( R_1 \) is connected between points \( A \) and \( E_C \).
- \( R_2 = 5 \text{ kOhm} \) is connected between points \( B \) and \( E_C \).
- \( R_3 = 27 \text{ kOhm} \) is connected between points \( A \) and \( E_D \).
- \( R_4 = 9 \text{ kOhm} \) is connected between points \( B \) and \( E_D \).

The bridge is powered by a voltage source \( E_s \) across points \( E_C \) and \( B \).

In the balanced condition, the potential difference \( E_0 \) between the junction points \( E_C \) and \( E_D \) is zero.

**Solution:**

For a Wheatstone bridge to be balanced, the following condition must be satisfied:

\[
\frac{R_1}{R_2} = \frac{R_3}{R_4}
\]

Substitute the known values:

\[
\frac{R_1}{5 \text{ kOhm}} = \frac{27 \text{ kOhm}}{9 \text{ kOhm}}
\]

Solving for \( R_1 \):

\[
R_1 = \frac{5 \times 27}{9} \text{ kOhm}
\]

Simplify to find:

\[
R_1 = 15 \text{ kOhm}
\]

Thus, the value of \( R_1 \) is \( 15 \text{ kOhm} \).

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