Components in Series Parallel and Combination Resistors in
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
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. R 1 R 2
Resistors in Circuits Series R 1 R 2 100 100 k 10 k 4. 7 k 330 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 R 1 R 2
Resistors in Circuits Parallel R 1 R 2 100 100 k 4. 7 k 330 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. § 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 R 1 R 2 R 3
Resistors in Circuits Mixed • Take the parallel segment of the circuit and calculate the equivalent resistance: R 1 R 2 R 3
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 The parallel resistors have been replaced by a single resistor with a value of 1498 ohms.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: R 1 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. • R 1 = 330 • R 2 = 1 k • R 3 = 2. 2 k • R 4 = 4. 7 k R 1 R 2 R 4 R 3
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 R 2 R 3
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 § RE = 3. 2 k-ohm • Now look at the parallel resistors RE and R 4. R 1 RE R 4
Resistors in Circuits Mixed • Using the parallel formula for: § RE = 3. 2 k-ohm § R 4 = 4. 7 k-ohm RE R 4
Resistors in Circuits Mixed • The final calculations involve R 1 and the new RTotal from the previous parallel calculation. § R 1 = 330 § RE = 1. 9 k R 1 RTotal
Resistors in Circuits Mixed R 1 = 330 ohm R 2 = 1 k-ohm RTotal = 2, 230 = R 4 = 4. 7 k-ohm R 3 = 2. 2 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
Capacitors in Circuits Parallel C 1 C 2 5000 p. F 750 p. F 100 p. F 0. 01 u. F 0. 047 u. F 100 u. F 50 u. F Calculated CE
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 5000 p. F 750 p. F 100 p. F 0. 01 u. F 0. 047 u. F 100 u. F 50 u. F Calculated CE
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 C 1 C 2 Parallel Series 5000 p. F 750 p. F 5750 p. F 652 p. F 100 p. F 200 p. F 50 p. F 0. 01 u. F 0. 047 u. F 0. 057 u. F 0. 008 u. F 100 u. F 50 u. F 150 u. F 33 u. F
Resistors in Series or Parallel • Now compare these trends to resistors. – Resistors in series are additive. – Resistors in parallel are fractional.
Resistors in Circuits R 1 R 2 Parallel Series 100 50 200 100 k 10 k 9. 09 k 110 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.
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