Components in Series, Parallel, and Combination
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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 Resistors in Circuits Series • Looking at the current path, if there is only one path, the components are in series. Resistors in Circuits 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 RE and measure the resistance with your VOM. R1 R2 Resistor Color Codes Resistors in Circuits Series R1 R2 100 100 100 k 10 k 4.7 k 330 4.7 k 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 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 4.7 k 330 10 k 10 k 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 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: 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: 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 The parallel resistors have been replaced by a single resistor with a value of 1498 ohms.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=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. • R1 = 330 • R2 = 1 k • R3 = 2.2 k • R4 = 4.7 k R1 R2 R4 R3 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 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 Resistors in Circuits Mixed • The final calculations involve R1 and the new RTotal from the previous parallel calculation. R1 = 330 RE = 1.9 k R1 RTotal Resistors in Circuits Mixed R1 = 330 ohm RTotal = 2,230 R2 = 1 k-ohm R3 = 2.2 k-ohm = R4 = 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 C1 C2 5000 pF 750 pF 100 pF 100 pF 0.01 uF 0.047 uF 100 uF 50 uF Calculated CE Pico = pF = 1 trillionth = 10-12 Micro = uF = 1 millionth = 10-6 Capacitors in Circuits Parallel C1 C2 5000 pF 750 pF Calculated CE 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 C1 C2 5000 pF 750 pF 100 pF 100 pF 0.01 uF 0.047 uF 100 uF 50 uF Calculated CE Capacitors in Circuits Series C1 C2 5000 pF 750 pF Calculated CE 652 pF 100 pF 100 pF 50 pF 0.01 uF 0.047 uF 0.008 uF 100 uF 50 uF 33 uF Resistors in Circuits (Let’s Review) R1 R2 100 100 100 k 10 k 4.7 k 4.7 k 330 4.7 k Parallel Series Resistors in Circuits (Let’s Review) 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.
