Resistors in CircuitsSeries
• Looking at the current path, if there is only one path, the components are in series.
Resistors in CircuitsSeries
• 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 CircuitsSeries
R1 R2 Calculated RE
Measured RE
100 100
100 k 10 k
4.7 k 4.7 k
330 4.7 k
Resistors in CircuitsParallel
• If there is more than one way for the current to complete its path, the circuit is a parallel circuit.
Resistors in CircuitsParallel
• 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
R1R2
Resistors in CircuitsParallel
R1 R2 Calculated RE
Measured RE
100 100
100 k 10 k
4.7 k 10 k
330 4.7 k
Resistors in CircuitsParallel 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
Resistors in CircuitsMixed
• 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
Series
Parallel
Resistors in CircuitsMixed
• Let’s start with a relatively simple mixed circuit. Build this using: R1 = 330
R2 = 4.7 k
R3 = 2.2 k
R1
R2R3
Resistors in CircuitsMixed
• Take the parallel segment of the circuit and calculate the equivalent resistance:
R1
R2R3
32
32
RR
RRRE
Resistors in CircuitsMixed
• 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 The parallel resistors have been replaced by a single resistor with a value of 1498 ohms.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:
ERR 1
R1
RE=1498
Resistors in CircuitsMixed
• 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
Series
Parallel
Series
R1
R2
R3
R4
Resistors in CircuitsMixed
• Looking at this portion of the circuit, the resistors are in series. R2 = 1 k-ohm
R3 = 2.2 k-ohm
R2
R3
32 RRRE
Resistors in CircuitsMixed
• 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 CircuitsMixed
• Using the parallel formula for: RE = 3.2 k-ohm
R4 = 4.7 k-ohm
RER4
4
4
RR
RRR
E
ET
Resistors in CircuitsMixed
• The final calculations involve R1 and the new RTotal from the previous parallel calculation. R1 = 330
RE = 1.9 k
R1
RTotal
ETotal RRR 1
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.
Capacitors in CircuitsParallel
C1 C2 Calculated CE
5000 pF 750 pF
100 pF 100 pF
0.01 uF 0.047 uF
100 uF 50 uF
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.
Capacitors in CircuitsSeries
C1 C2 Calculated CE
5000 pF 750 pF
100 pF 100 pF
0.01 uF 0.047 uF
100 uF 50 uF
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