Circuits 1
Fall 2005
Harding University
Jonathan White

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Node definition
KCL
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The current entering a node is equal to the current leaving a node.
KVL
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The sum of voltages around a closed loop is 0.
Series circuits
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Resistors in series add
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R eq is always greater than R1 and R2
Voltage Dividers
Parallel circuits
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Resistors in parallel follow the equation R eq
R eq is always less than R
1 and R
2
= (R
1
*R
2
)/(R
1+
R
2).

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A node is where 2 or more elements meet.
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For now, and element can be a resistor, a voltage source, or a current source.
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Each point in the node must be electrically the same.
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Exp:

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A fundamental law of nature, like the Law of
Conservation of Mass.
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KCL is the conservation of charge – charge can neither be created or destroyed.
KCL definition: The sum of all currents entering a node is equal to the sum of all currents leaving the node.
KCL holds for every node in a network and it works at every point in time.

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Write equations for the current in each of the nodes in the circuit below:

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A fundamental law of nature, like the Law of
Conservation of Energy.
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KVL is the conservation of electrical energy – electrical energy can neither be created or destroyed, only transferred.

1.
2.
3.
4.
5.
6.
As the charge moves from the top of the battery to the top of Element #1 (along the wire shown in purple), how much energy does the charge lose?
As the charge moves from the top of Element #1 through Element #1 to the bottom of element #1, how much energy does the charge lose?
As the charge moves from the bottom of Element
#1 to the top of Element #2, how much energy does the charge lose?
As the charge moves from the top of Element #2 through Element #2 to the bottom of element #2, how much energy does the charge lose?
As the charge moves from the bottom of Element
#2 to the bottom of the battery, how much energy does the charge lose?
As the charge moves from the bottom of the battery through the battery to the top of the battery, how much energy does the charge lose?

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What is V b equal to?
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KVL definition: the sum of voltages around a closed loop is
0.

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Write all the KVL equations for the circuit below:

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2 devices are said to be in series when the same current physically flows through both.
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Current flows into one element, through the element, out of the element into the other element, through the second element and out of the second element. No part of the current that flows through one resistor "escapes" and none is added.
You see series resistance everyday

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Consider the simplest series resistance:
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What is Vs ?
The equivalent resistance for resistors in series is always the sum of the individual resistors.

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Used as volume controls in electronic devices
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Provides a continuous sound spectrum, i.e., not digital.
Used in RC combinations to filter out input noise in devices such as tachometers and …
A voltage divider looks like this:

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How much current flows through R a and R b
? Use Ohm’s Law.
What is V out
?
As R b
V out goes to 0, what’s the value of
? R b is then physically like what?
As R b
V out goes to ∞, what’s the value of
? R b is then physically like what?

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2 resistors are in parallel if the same physical voltage appears across each resistor.
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Each resistor provides its own path for the flow of current. If the resistors have different resistance values, they will carry different amounts of current, each in accordance with Ohm's Law.

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Consider the simplest parallel resistance to the right. What is I p
?
In parallel resistors, the equivalent resistance is always lower than either of the resistors.