Download Document

Components in Series, Parallel,
and Combination
Resistors in Circuits
Series
• Looking at the
current path, if
there is only one
path, the
components are in
series.
Resistors in Circuits
Series
RE  R1  R2  Rn
Resistors in Circuits
Series
• On your proto board set up
the following circuit using
the resistance values
indicated on the next slide.
• Calculate the equivalent
resistant RE and measure
the resistance with your
VOM.
R1
R2
Resistors in Circuits
Series
R1
R2
100
100
100 k
10 k
4.7 k
4.7 k
330
4.7 k
Calculated Measured
RE
RE
Resistors in Circuits
Parallel
• If there is more
than one way for
the current to
complete its path,
the circuit is a
parallel circuit.
Resistors in Circuits
Parallel
R1R2
1
RE 

1
1
1
R1  R2


R1 R2 Rn
Resistors in Circuits
Parallel
• On your proto board set
up the following circuit
using the resistance
values indicated on the
next slide.
• Calculate the equivalent
resistant RE and measure
the resistance with your
VOM
R1
R2
Resistors in Circuits
Parallel
R1
R2
100
100
100 k
10 k
4.7 k
10 k
330
4.7 k
Calculated Measured
RE
RE
Resistors in Circuits
Parallel Challenge
• Make a circuit with 3 resistors in parallel,
calculate the equivalent resistance then
measure it.
 R1 = 330 ohm
 R2 = 10 k-ohm
 R3 = 4.7 k-ohm
Series
• If the path for the
current in a portion
of the circuit is a
single path, and in
another portion of
the circuit has
multiple routes, the
circuit is a mix of
series and parallel.
Series
Resistors in Circuits
Mixed
Parallel
Resistors in Circuits
Mixed
• Let’s start with a
relatively simple
mixed circuit.
Build this using:
 R1 = 330
 R2 = 4.7 k
 R3 = 2.2 k
R1
R2
R3
Resistors in Circuits
Mixed
• Take the parallel
segment of the
circuit and
calculate the
equivalent
resistance:
R2 R3
RE 
R2  R3
R1
R2
R3
Resistors in Circuits
Mixed
• We now can look at
the simplified circuit
as shown here. The
parallel resistors have
been replaced by a
single resistor with a
value of 1498 ohms.
• Calculate the
resistance of this
series circuit:
R1  RE
R1
RE=1498
Resistors in Circuits
Mixed
Series
R1
R2
R4
R3
Parallel
Series
• In this problem,
divide the problem
into sections, solve
each section and
then combine them
all back into the
whole.
• R1 = 330
• R2 = 1 k
• R3 = 2.2 k
• R4 = 4.7 k
Resistors in Circuits
Mixed
• Looking at this
portion of the
circuit, the resistors
are in series.
 R2 = 1 k-ohm
 R3 = 2.2 k-ohm
RE  R2  R3
R2
R3
Resistors in Circuits
Mixed
• Substituting the
equivalent resistance
just calculated, the
circuit is simplified to
this.
 R1 = 330 ohm
 R4 = 4.7 k-ohm
 RE = 3.2 k-ohm
• Now look at the parallel
resistors RE and R4.
R1
RE
R4
Resistors in Circuits
Mixed
• Using the
parallel formula
for:
 RE = 3.2 k-ohm
 R4 = 4.7 k-ohm
RE R4
RT 
RE  R4
RE
R4
Resistors in Circuits
Mixed
• The final calculations
involve R1 and the new
RTotal from the previous
parallel calculation.
 R1 = 330
 RE = 1.9 k
RTotal  R1  RE
R1
RTotal
Resistors in Circuits
Mixed
R1 = 330 ohm
RTotal = 2,230
R2 = 1 k-ohm
=
R4 = 4.7 k-ohm
R3 = 2.2 k-ohm
Inductors
• Inductors in series, parallel, and mixed circuits
are treated exactly the same as resistors
mathematically so the same formulas and
techniques apply.
• Capacitors on the other hand are the exact
opposite mathematically.
Capacitors in Circuits
• The amount of capacitance depends on:
– Surface area of parallel conductive plates.
– Space between plates.
– Dielectric (material between plates).
• The math for finding equivalent capacitance is
opposite from the math for resistors.
– Think of plate surface area.
– Think of space between plates.
Parallel Capacitance
• When capacitors are connected in parallel, the
top plates are connected together and the
bottom plates are connected together.
• This means that the top surface areas are
combined (added) and the bottom surfaces are
combined (added).
• Greater surface area therefore means greater
capacitance.
Parallel Capacitance
C1  C2  C3  CN  CT
Capacitors in Circuits
Parallel
C1
C2
5000 pF
750 pF
100 pF
100 pF
0.01 uF
0.047 uF
100 uF
50 uF
Calculated
CE
Series Capacitance
• When capacitors are connected in series, the
top plates are connected to the bottom plates of
the adjacent capacitor.
• This means that the top plate of the first
capacitor is further away from the bottom plate
of the last capacitor.
• The greater the distance between the plates in a
capacitor the lower the capacitance.
Series Capacitance
1
1
1
1
1



C1 C2 C3 C N
C1C2
 CT
C1  C2
 CT
Capacitors in Circuits
Series
C1
C2
5000 pF
750 pF
100 pF
100 pF
0.01 uF
0.047 uF
100 uF
50 uF
Calculated
CE
Capacitors in Series or Parallel
• Compare the results of the previous two math
exercises.
– Capacitors in parallel are additive.
– Capacitors in series are fractional.
Capacitors in Circuits
C1
C2
Parallel
Series
5000 pF
750 pF
5750 pF 652 pF
100 pF
100 pF
200 pF
50 pF
0.01 uF 0.047 uF 0.057 uF 0.008 uF
100 uF
50 uF
150 uF
33 uF
Resistors in Series or Parallel
• Now compare these trends to resistors.
– Resistors in series are additive.
– Resistors in parallel are fractional.
Resistors in Circuits
R1
R2
Parallel
Series
100
100
50
200
100 k
10 k
9.09 k
110 k
4.7 k
4.7 k
2.35 k
9.4 k
330
4.7 k
308
5.03 k
Major Learning Hint
• The point is, learn one set of formulas (for
resistance), and just know that capacitors are
the opposite (mathematically) of resistors.