# DC Circuits*

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: $V_{R_1}=\frac{R_1}{R_1+R_2} V$ Problem 2. In the Whetstone bridge given in the figure above, R1 and R2  are given, R is a resistor with variable resistance and Rx is unknown. If the potential difference between points b and d is zero, prove that $\frac{R_1}{R_x}= \frac{R_2}{R}\;\;\;\;(\text{Eq.1})$

*Hint: Use your results from Problem 1 to compare the voltage across R1 and Rx, which should be equal if the potential difference between points b and d is zero.

#### 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.

R1=20Ω , R2=40Ω , R3=10Ω , and V = 10 V

Using the voltmeter, measure the voltage across each element.

Measure the current through resistors:

• Break the connection between R1 and junction p. A and connect an ammeter. Record the value of the current through R1.
• Break the connection between R2 and junction p. A and connect an ammeter. Record the current through R2.
• Break the connection between R3 and junction p.A and connect an ammeter. Record the current through R3.
##### Data and Results

Record your measurements in a table. Show that  (a) the total current through R1 and R2 equals to that through R3, and (b) the sum of the voltages across R1 and R3 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:

R1=20Ω , R2=16Ω , and V = 10 V

Leave  R3  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.