April 21 DC Circuits

Purpose: In todays class, we began our studies of direct circuits (DC). A direct current is the unidirectional flow of electric charge, which is usually produced by sources such as batteries. Direct current flows in a conductor such as a wire, and its current flows in a constant direction which is what makes it different from AC circuits. We discussed how DC circuits work in series and in parallel, and how resistors work in such circuits and how they are color coded in order to be read.

We began with the discussion of voltage and current in a DC circuit. We were asked to make some predictions of what would happen if the switch was closed instead of open in each scenario pictured below. 

Our prediction for this one was that all three light bulbs would light up. After conducting the experiment, we found our predictions to be incorrect. This is because the center of the circuit is negligible; the current flows on the outer part of the circuit. 

Our prediction here was that the upper light bulb would become dimmer and the lower light bulb would become brighter.
After experimentation, we found that there was no change. 

Final conclusion to experiment was that there was no change on the light bulbs in this DC circuit when the switch was closed. The reason for this is that voltage in a parallel circuit is the same throughout the whole circuit, it remain constant.



Our next activity we were asked the following:

Activity:  As a table have one half setup the two batteries and two bulbs from last week to make the bulbs as bright as possible.  Have the other half setup the bulbs to make them as dim as possible.  Observe the circuits and complete the following table:

Circuit Element Series / Parallel

Dim Bulbs Seeries
Bright Bulbs Parallel

Bright Bulbs Parallel

Dim Batteries Parallel

Bright Batteries series

Using a Multimeter

A digital multimeter is a device that can be used to measure either current, voltage, or resistance depending on how it is set up.  

SERIES CIRCUITS

We will start by making measurements of the current and voltage of your circuits

 VOLTAGE

 Measure the voltage across each of the batteries as shown.  First use both batteries in series, followed by just one battery.  

# Batteries	Voltage of source	VR1	VR2
1	1.26	0.62	0.62
2	2.55	1.26	1.26

# Batteries

Voltage of source

VR1

    VR2

1

1.26

0.62

     0.62

2

2.55

1.26

     1.26

Write a relationship between the voltage of the source (batteries) and the voltage across  the bulbs. 

The sum of the resistors is equal to the source of voltage.

2.  Use the same circuit as before EXCEPT put ammeters in positions 1, 2, and 3 in the circuit.

# Batteries

Voltage of source

I1 (A)

I2 (A)

I3 (A)

1			1.26            1.01     1.01	1.01
2			2.05              2.05    2.05	2.05

PARALLEL CIRCUITS.

1. Now measure the voltage across each of the bulbs and the batteries as shown.  

# Batteries	Voltage of source	VR1	VR2
1	1.26	1.26	1.26
2	2.55	2.55	2.55

2.  Use the same circuit as before EXCEPT put ammeters in positions 1, 2, and 3 in the circuit. 

#batteries	I1(A)	I2(A)	I3 (A)
1	2.0	2.0	2.0
2	4.0	4.0	8.1

Important rules in solving circuit problems:

components in a series circuit will have the same current throughout and voltage will divide.

Components connected in parallel will have the same voltage throughout and current will divide. 

Resistance and Its Measurement

For our next activity, we continue with the study of resistors. A resistor is a electrical component that induces electrical resistance as a circuit element. In our pervious activities and experiments, we created circuits which involved the use of light bulbs. Light bulbs are a perfect example of a type of resistor. Electrical energy is transferred to light and heat energy inside a light bulb when connected to a circuit, and even though all the current returns to the battery after flowing through the light bulb, potential energy has been lost. Potential energy has been lost because the light bulb puts resistance on the flow of electric current, thus, a light bulb is one kind of electrical resistance. However, a light bulb has a resistance that increases with temperature and current, so they do not made a good circuit element. To get a better understanding of resistors, we examine carbon resistors. Using Ohm's law, we have an equation for resistance in terms of potential difference and current, which is: R=V/I. We were told that carbon resistors will have a constant R for a range of different currents, which doesn't apply to light bulbs which is why they make poor ohmic resistors. Carbon resistors are measured in Ohms's. A carbon resistor usually has colored markings around it to signify its value in ohms

Here we have a detailed description of carbon resistors. The last band on a carbon resistor signifies its tolerance and the orientation of the other colors can tell us the resistance level which can be calculated by if equation: value in ohms = AB × 10^c ± D.   

Activity:  Decoding and Measuring Resistors

a. Decode the five resistors, determine the resistance of each.

Here we calculated the resistance of each resistor by hand using each one's color band orientation.

Here we have a resistor close up and as you can see the tolerance of this +/- 5, because it has a gold band at the end. We then measured the resistance of each resistor with a multimeter to find if our theoretical values match our experimental.

A blog question we were given was: Did the resistors match the colored coded value within the uncertainty.
The answer to this question was yes, the values we calculated by hand (pictured above) did in fact match the experimental.

Carbon Resistors in Parallel and Series

Activity:  Resistances for Series Wiring

a. If you have three different carbon resistors, what do you think the equivalent resistance to the flow of electrical current will be if the resistors are wired in series?  Explain the reasons for your prediction based on your previous observations with batteries and bulbs.

answer: we said that resistors would add together

b. Compare the calculated and measured values of equivalent resistance of the series network as follows:  

Write down the measured values of each of the three resistors:

R₁ =  ________________________  Ω

R₂ =  ________________________  Ω

R₃ =  ________________________  Ω

Our values for part b

Here we have our resistors in parallel and in series with our measured value noted right below each corresponding diagram. What we found was that when resistors are in series the total resistance is its sum of all the resistors. However, when resistors are in parallel, the total resistance is the sum of the inverse of each resistor. 

Note:the resistance of carbon resistors doesn’t change as current is increased

Kirchhoff’s Laws

WWe move on with our study of Kirchhoff's Law. In the real work circuits are not all simple, in fact they are usually set in a combination of series and parallel which may contain an X amount of resistors. In order to analyze a circuit we use something called Kirchhoff's Laws, Which are as follows:

Kirchhoff’s Laws

1. Junction (or node) Rule (based on charge conservation):  The sum of all the currents entering any node or branch point of a circuit (that is, where two or more wires merge)must equal the sum of all currents leaving the node.

2. Loop Rule (based on energy conservation):  Around any closed loop in a circuit, the sum of all emfs, voltage gains provided by batteries or other power sources, (ε = emf) and all the potential drops across resistors and other circuit elements must equal zero.

We were given as example of how to use Kirchhoff's Laws which is pictures below. We were given an outline of how to perform such calculation. First, we assign currents, next apply the loop rule -/+ through 1/r + V and finally indicate direction of current of loop with respect to V.