Post on 17-Jan-2016
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Resistance and Ohm’s Law: More Practice
Resistance and Ohm’s Law: More Practice
Resistance and Ohm’s Law: More Practice
Resistance and Ohm’s Law: More Practice
Kirchoff’s Laws:Success Criteria I can state Kirchhoff's laws and Ohm's law
and use them to explain, in quantitative terms, direct current, potential difference, and resistance in mixed circuit diagrams.
I can construct real and simulated mixed direct current circuits and analyse them in quantitative terms to test Ohm's and Kirchhoff's laws.
Kirchoff’s Laws and Equivalent ResistanceSPH4C
Kirchoff’s Current Law
At any junction point in an electrical circuit, the total current into the junction equals the total current out of the junction.
Kirchoff’s Current Law
At any junction point in an electrical circuit, the total current into the junction equals the total current out of the junction.
(“What goes in must come out.”)
In the diagram at right,
I1 + I2 = I3
Kirchoff’s Voltage Law
In any complete path in an electrical circuit, the sum of the potential increases equals the sum of the potential drops.
Kirchoff’s Voltage Law
In any complete path in an electrical circuit, the sum of the voltage increases equals the sum of the voltage drops.
(“What goes up must come down.”)
The Laws for a Series Circuit
The current is the same at all points in the circuit:
IT = I1 = I2 = . . .
The total voltage supplied to the circuit is equal to the sum of the voltage drops across the individual loads:
VT = V1 + V2 + . . .
Equivalent Resistance in SeriesGiven
VT = V1 + V2 + . . .
Equivalent Resistance in SeriesGiven
VT = V1 + V2 + . . .
From Ohm’s Law, V = IR
ITRT = I1R1 + I2R2 + . . .
Equivalent Resistance in SeriesGiven
VT = V1 + V2 + . . .
From Ohm’s Law, V = IR
ITRT = I1R1 + I2R2 + . . .
Since IT = I1 = I2 = . . .
IRT = IR1 + IR2 + . . .
Equivalent Resistance in SeriesGiven
VT = V1 + V2 + . . .
From Ohm’s Law, V = IR
ITRT = I1R1 + I2R2 + . . .
Since IT = I1 = I2 = . . .
IRT = IR1 + IR2 + . . .
Divide all terms by I and the equivalent resistance is the sum of the individual resistances:
Req or RT = R1 + R2 + . . .
Series Resistance Example
Series Resistance Example
Req = R1 + R2 + R3
Series Resistance Example
Req = R1 + R2 + R3
Req = 17 + 12 + 11 = 40
Series Resistance Example
IT = VT/Req
Series Resistance Example
IT = VT/Req
IT = 60 V/40 = 1.5 A
Series Resistance Example
IT = VT/Req
IT = 60 V/40 = 1.5 A
And I1 = I2 = I3 = IT = 1.5 A
Series Resistance Example
V1 = I1R1 = (1.5 A)(17 ) = 25.5 V
V2 = I2R2 = (1.5 A)(12 ) = 18 V
V3 = I3R3 = (1.5 A)(11 ) = 16.5 V
The Laws for a Parallel Circuit
At a junction:
IT = I1 + I2 + . . .
But the total voltage across each of the branches is the same:
VT = V1 = V2 = . . .
Equivalent Resistance in Parallel
Given
IT = I1 + I2 + . . .
From Ohm’s Law, V = IR or I = V/R
VT/RT = V1/R1 + V2/R2 + . . .
Since VT = V1 = V2 = . . .
V/RT = V/R1 + V/R2 + . . .
Divide all terms by V and the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances:
1/Req or 1/RT = 1/R1 + 1/R2 + . . .
Equivalent Resistance in Parallel
1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = 1/(12 ) + 1/(12 ) + 1/(12 )
Using a calculator ...
1/Req = 0.25 -1
Req = 1 / (0.25 -1)
Req = 4.0
Equivalent Resistance in Parallel
1/Req = 1/R1 + 1/R2 + 1/R3
Equivalent Resistance in Parallel
1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = 1/(5.0 ) + 1/(7.0 ) + 1/(12 )
1/Req = 0.42619 -1
Req = 1 / (0.42619 -1)
Req = 2.3
Combination Circuits
What do we do if a circuit has both series and parallel loads?
Find the equivalent resistance of the loads in parallel and continue the analysis. E.g.:
More Practice
Equivalent Resistance Lab Activity