Components in Series, Parallel, and Combination

Resistors in CircuitsSeries

• Looking at the current path, if there is only one path, the components are in series.

Resistors in CircuitsSeries

nE RRRR 21

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

n

E

RRRRR

RRR

1111

21

21

21

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 The parallel resistors have been replaced by a single resistor with a value of 1498 ohms.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

Resistors in CircuitsMixed

R1 = 330 ohm

R2 = 1 k-ohm

R3 = 2.2 k-ohm

R4 = 4.7 k-ohm

RTotal = 2,230

=

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

TN CCCCC 321

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.

Series Capacitance

T

N

C

CCCC

1111

1

321

TCCC

CC

21

21

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

Major Learning Hint

• The point is, learn one set of formulas (for resistance), and just know that capacitors are the opposite (mathematically) of resistors.