Introduction(Kcl Kvl)
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Transcript of Introduction(Kcl Kvl)
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Introduction
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Example
Kirchoffs Voltage Law around 1stLoop
+
-Vs
Is
R1
R2 R3
+
Vo
-
A B
C
I2
I1
+
I2R2
-
+ I1R1 -
Assign current variables and directions
Use Ohms law to assign voltages and polarities consistent with
passive devices (current enters at the + side)
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Example
Kirchoffs Voltage Law around 1stLoop
+
-Vs
Is
R1
R2 R3
+
Vo
-
A B
C
I2
I1
+
I2R2
-
+ I1R1 -
Starting at node A, add the 1stvoltage drop: + I1R1
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Example
Kirchoffs Voltage Law around 1stLoop
+
-Vs
Is
R1
R2 R3
+
Vo
-
A B
C
I2
I1
+
I2R2
-
+ I1R1 -
Add the voltage drop from B to C through R2: + I1R1+ I2R2
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Example
Kirchoffs Voltage Law around 1stLoop
+
-Vs
Is
R1
R2 R3
+
Vo
-
A B
C
I2
I1
+
I2R2
-
+ I1R1 -
Subtract the voltage rise from C to A through Vs: + I1R1+ I2R2Vs = 0
Notice that the sign of each term matches the polarity encountered 1st
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Kirchoffs Current Law (KCL)
The algebraic sum of currents entering a node
is zero
Add each branch current entering the node and
subtract each branch current leaving the node
currents in - currents out = 0
Or currents in = currents out
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Example
Kirchoffs Current Law at B
+
-Vs
Is
R1
R2 R3
+
Vo
-
AB
C
I2
I1
Assign current variables and directions
Add currents in, subtract currents out: I1I2I3+ Is = 0
I3
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Series Circuit
Series circuit - has only one path through
which the electricity can flow.
In the above diagram, the electricity flows
through both loads.
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Current and Resistance in Series Circuits
For the series circuit the same current flows throughboth loads.
The loads can be added together to calculate the
total load. Rtot = R1 + R2, where Rtot is the total resistance, R1is the resistance of one load, and R2 is the resistanceof the other.
The total load (resistance) in a series circuit with nloads is the sum of the resistance of the n objects.Rtot = R1 + R2 + + Rn.
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Total Voltage in a Series Circuit
Ohms Law can be used to calculate the total
voltage in a series circuit by calculating the
sum of the voltage parts.
V = V1 + V2, where V is the total voltage
(battery voltage), V1 is the voltage at the first
load, and V2 is the voltage at the other load.
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Parallel Circuits
A parallel circuithas multiple paths through
which the electricity can flow.
In a parallel circuit, the current though one
path may be different than the current
through the other path.
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Resistance in Parallel Circuits
Using Ohms Law you can derive a formula forthe equivalent resistance of two resistors inparallel.
I1 = V/R1 I2 = V/R2
I = I1 + I2 = V/R1 + V/R2
= (VR2 + VR1)/R1R2 = V(R2+R1)/R1R2 Rtot = V/(V(R2+R1)/ R1R2 = R1R2/(R1+R2)
