Components in Series, Parallel, and Combination

Components in Series, Parallel, and Combination

Kirchoff s Laws VOLTAGE LAW: A series circuit of voltages across the various components must add up to be equal to the voltage applied to the circuit. CURRENT LAW: The total current entering a circuit junction must equal the sum of currents leaving the junction.

Kirchoff s Laws Page 4-14

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

Series

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. R 1 R 2

Resistor Color Codes

Series R 1 R 2 Calculated R E 100 100 100 k 10 k 4.7 k 4.7 k 330 4.7 k Measured R E

Parallel If there is more than one way for the current to complete its path, the circuit is a parallel circuit.

Parallel

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 R 1 R 2

Parallel R 1 R 2 Calculated R E 100 100 100 k 10 k 4.7 k 10 k 330 4.7 k Measured R E

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

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. Mixed

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 R 1 R 2 R 3

Mixed Take the parallel segment of the circuit and calculate the equivalent resistance: R 1 R 2 R 3

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 The parallel resistors have been replaced by a single resistor with a value of 1498 ohms.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: R 1 R E =1498

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 R 1 R 2 R 3 R 4

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

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. R 1 R E R 4

Mixed Using the parallel formula for: R E = 3.2 k-ohm R 4 = 4.7 k-ohm R E R 4

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 R 1 R Total

R 1 = 330 ohm Resistors in Circuits Mixed R Total = 2,230 R 2 = 1 k-ohm R 3 = 2.2 k-ohm = R 4 = 4.7 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

Capacitance Typical Values (in Farads) Pico = pf = 1 trillionth = 10-12 Micro = uf = 1 millionth = 10-6 Pico = 0.000000000001 Micro = 0.000001

Capacitors in Circuits Parallel C 1 C 2 Calculated C E 5000 pf 750 pf 100 pf 100 pf 0.01 uf 0.047 uf 100 uf 50 uf Pico = pf = 1 trillionth = 10-12 Micro = uf = 1 millionth = 10-6

Capacitors in Circuits Parallel C 1 C 2 Calculated C E 5000 pf 750 pf 5750 pf 100 pf 100 pf 200 pf 0.01 uf 0.047 uf 0.057 uf 100 uf 50 uf 150 uf Pico = pf = 1 trillionth = 10-12 Micro = uf = 1 millionth = 10-6

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 C 1 C 2 Calculated C E 5000 pf 750 pf 100 pf 100 pf 0.01 uf 0.047 uf 100 uf 50 uf

Capacitors in Circuits Series C 1 C 2 Calculated C E 5000 pf 750 pf 652 pf 100 pf 100 pf 50 pf 0.01 uf 0.047 uf 0.008 uf 100 uf 50 uf 33 uf

(Let s Review) R 1 R 2 Parallel Series 100 100 100 k 10 k 4.7 k 4.7 k 330 4.7 k

(Let s Review) R 1 R 2 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.