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

On your proto board set up the following circuit using the resistance values indicated on the next slide. Calculate the equivalent resistant R E and measure the resistance with your VOM. R1R1 R2R2

Resistors in Circuits Series R1R1 R2R2 Calculated R E Measured R E k10 k 4.7 k k

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

On your proto board set up the following circuit using the resistance values indicated on the next slide. Calculate the equivalent resistant R E and measure the resistance with your VOM R1R1 R2R2

Resistors in Circuits Parallel R1R1 R2R2 Calculated R E Measured R E k10 k 4.7 k10 k k

Resistors in Circuits Parallel Challenge Make a circuit with 3 resistors in parallel, calculate the equivalent resistance then measure it.  R 1 = 330 ohm  R 2 = 10 k-ohm  R 3 = 4.7 k-ohm

Resistors in Circuits Mixed 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.

Resistors in Circuits Mixed Let’s start with a relatively simple mixed circuit. Build this using:  R 1 = 330  R 2 = 4.7 k  R 3 = 2.2 k R1R1 R2R2 R3R3

Resistors in Circuits Mixed Take the parallel segment of the circuit and calculate the equivalent resistance: R1R1 R2R2 R3R3

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 The parallel resistors have been replaced by a single resistor with a value of 1498 ohms.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: R1R1 R E =1498

Resistors in Circuits Mixed In this problem, divide the problem into sections, solve each section and then combine them all back into the whole. R 1 = 330 R 2 = 1 k R 3 = 2.2 k R 4 = 4.7 k R1R1 R2R2 R3R3 R4R4

Resistors in Circuits Mixed Looking at this portion of the circuit, the resistors are in series.  R 2 = 1 k-ohm  R 3 = 2.2 k-ohm R2R2 R3R3

Resistors in Circuits Mixed Substituting the equivalent resistance just calculated, the circuit is simplified to this.  R 1 = 330 ohm  R 4 = 4.7 k-ohm  R E = 3.2 k-ohm Now look at the parallel resistors R E and R 4. R1R1 RERE R4R4

Resistors in Circuits Mixed Using the parallel formula for:  R E = 3.2 k-ohm  R 4 = 4.7 k-ohm RERE R4R4

Resistors in Circuits Mixed The final calculations involve R 1 and the new R Total from the previous parallel calculation.  R 1 = 330  R E = 1.9 k R1R1 R Total

Resistors in Circuits Mixed R 1 = 330 ohm R 2 = 1 k-ohm R 3 = 2.2 k-ohm R 4 = 4.7 k-ohm R Total = 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

Capacitors in Circuits Parallel C1C1 C2C2 Calculated C E 5000 pF750 pF 100 pF 0.01 uF0.047 uF 100 uF50 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

Capacitors in Circuits Series C1C1 C2C2 Calculated C E 5000 pF750 pF 100 pF 0.01 uF0.047 uF 100 uF50 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 C1C2ParallelSeries 5000 pF750 pF5750 pF652 pF 100 pF 200 pF50 pF 0.01 uF0.047 uF0.057 uF0.008 uF 100 uF50 uF150 uF33 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 R1R1 R2R2 ParallelSeries k10 k9.09 k110 k 4.7 k 2.35 k9.4 k k 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.