This is an online simulation that uses University of Colorado PhET Circuit Construction (DC) Kit applet.

##### Purpose

To determine an unknown resistance using Whetstone bridge.

#### Objectives

- To determine the rules for the electric current and how it splits through resistors in DC circuits
- To determine how voltage across resistors changes in DC Circuits
- To learn how to use Whetstone bridge to determine unknown resistance
- To learn how ammeters and voltmeters are used in circuits to measure current and voltage, respectively

#### Theory

*Problem 1. *If the electric potential difference between points a and c is given as *V*, prove that the voltage across the first resistor is:

*Problem 2. *In the Whetstone bridge given in the figure above, *R _{1}* and

*R*are given

_{2}*is a resistor with variable resistance and R*

*,**R*_{x}is unknown. If the potential difference between points b and d is zero, prove that

*Hint: Use your results from Problem 1 to compare the voltage across *R _{1}* and

*R*, which should be equal if the potential difference between points b and d is zero.

_{x}#### Activity 1. Electric current through and voltage across resistors in DC circuits

Using the PhET Circuit Simulation (DC) Kit, built the circuit on the diagram.

*R _{1}=20Ω , *

*R*and

_{2}=40Ω , R_{3}=10Ω ,*V = 10 V*

Using the voltmeter, measure the voltage across each element.

Measure the current through resistors:

- Break the connection between
*R*and junction p. A and connect an ammeter. Record the value of the current through_{1}*R*._{1} - Break the connection between
*R*_{2}and junction p. A and connect an ammeter. Record the current through*R*._{2} - Break the connection between
*R*and junction p.A and connect an ammeter. Record the current through_{3}*R*._{3}

##### Data and Results

Record your measurements in a table. Show that (a) the total current through *R _{1}* and

*R*equals to that through

_{2}*R*, and (b) the sum of the voltages across R

_{3}_{1}and R

_{3}equals to that of the battery.

#### Activity 2. Find the value of an unknown resistance

##### Theory

Construct a Whetstone Bridge circuit following the diagram:

Use the following values for the resistances and the battery:

*R _{1}=20Ω , *

*R*and

_{2}=16Ω ,*V = 10 V*

Leave * R _{3} *

*unchanged and unknown.*

*Connect the voltmeter across points A and B, and adjust the resistance of the lightbulb until the voltmeter measures 0.0 V.*

##### Results

Use Eq.1 to determine *R* and check with the simulation to see if its value is identical to what you calculated.

Submit your solution to Problems 1 and 2, as well as your results from Activities 1 and 2 for a lab grade.