power, simple circuits, resistor combinationspages.erau.edu/~snivelyj/ps250/ps250-lecture14.pdf ·...
TRANSCRIPT
PS 250: Lecture 14 Power, Simple Circuits, Resistor Combinations
J. B. Snively September 30th, 2015
Today’s Class
Energy and Power Resistors in Series and Parallel Kirchhoff’s Rules for Circuit Calculations Summary
Rate of energy transfer [J]/[s] = [W]
Recall: Volts [J]/[C], Amperes [C]/[s]
“Rate [per second] at which energy [Joules] is delivered or extracted from a circuit element”
Power (Rate of Energy Transfer)
P = VabI[J]
[C]
[C]
[s]=
[J]
[s]= [W]
Power Dissipation of Resistors
First, recall that:P = VabI and Vab = IR
By substituting in Ohm’s Law, we can obtain:
P = VabI = I2R =V 2ab
R
In a resistor, power is dissipated as heat! Practical resistors have a max power rating.
Today’s Class
Energy and Power Resistors in Series and Parallel Kirchhoff’s Rules for Circuit Calculations Summary
Series Combination: Equal current through
each resistor.
Parallel Combination: Equal potential
difference across each resistor.
R2R1
R2R1
Combinations of Resistors
V
V
+
-
+
-
I
Series Resistors
...RNR2R1
V+
-
Current through each resistor is constant:V = IR1 + IR2 + ...IRN = I(R1 +R2 + ...RN )
Series Equivalent Resistance REQ:
REQ = R1 +R2 + ...RN
I
Parallel Resistors
RN...R2R1V+
-
Potential difference across each resistor is constant:I =
V
REQ=
V
R1+
V
R2+ ...
V
RN
Parallel Equivalent Resistance REQ:1
REQ=
1
R1+
1
R2+ ...
1
RN
Today’s Class
Energy and Power Resistors in Series and Parallel Kirchhoff’s Rules for Circuit Calculations Summary
The algebraic sum of the currents into an junction (“node”) is zero:
The algebraic sum of the potential differences in any loop is zero:
Kirchhoff’s Rules
XI = 0
XV = 0
Junction Rule:
RN...R2R1V+
-
Sum of the currents entering and leaving a junction point (“node”) equals zero:
XI = Isrc �
V
R1� V
R2� ...
V
RN= 0
Loop Rule:
...RNR2R1
Vsrc+
-
Sum of the potential differences across each source and resistor equals zero:
I
XV = Vsrc � IR1 � IR2 � ...IRN = 0
Applies to all circuits (assuming no external time-varying magnetic flux).
Can be used to find individual currents (or potentials) through (or across) circuit elements in complex configurations.
Can be used for circuits with multiple sources and multiple loops or nodes.
When multiple loops or nodes are present, it becomes necessary to solve simultaneous equations.
Kirchhoff’s Rules
Summary / Next Class:
Homework for Friday
Prepare to discuss 26.4.