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Electrical Circuits

Electrical Circuits. ~Moving Charge Put to Use. Zap!. A. V. The Circuit. All circuits, no matter how simple or complex, have one thing in common, they form a complete loop. As mentioned before, circuits should have various circuit elements in the loop. 4 x 4. Series Circuit.

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Electrical Circuits

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  1. Electrical Circuits ~Moving Charge Put to Use

  2. Zap! A V The Circuit • All circuits, no matter how simple or complex, have one thing in common, they form a complete loop. • As mentioned before, circuits should have various circuit elements in the loop.

  3. 4 x 4 Series Circuit • Have you ever driven down a 1 lane road? • You can keep moving until… • If there is an accident all traffic stops, there is no other road to follow.

  4. R1 R2 Series Circuit • A series circuit is similar to a one lane road, current can flow in only one path. • Even if you add a 2nd resistor in series, there is still just 1 path.

  5. Series Circuit • One path means all components have the same current • The Voltage provided by the source must equal the Voltage drop across the resistor(s) I V R

  6. Series Circuit • One path means all components have the same current • What is the voltage drop across R1? R1 I V R2

  7. Req V Series Circuit • How do we find Req? Divide both sides by Is R1 I V R2

  8. R1 R2 Req The Series Circuit (cont.) • Every series configuration can be reduced to a single value for resistance known as the equivalent resistance, or Req. • The formula for Req is as follows for series: • This can be used as a step to solve for the current in the circuit or the voltage across each resistor. I

  9. Ieq = 0.1A 10W 20W 6V 60W 6V 30W Sample Problem (Series) • A circuit is configured in series as shown below. • What is the equivalent resistance (Req)? • What is the current through the circuit? (Hint: Use Ohm’s Law.)

  10. Ieq = 0.1A 10W 20W 6V 30W Sample Problem (Series) (cont.) • We still have one question to ask. What are the voltages across each resistor? • For the 10W Resistor: • For the 20W Resistor: • For the 30W Resistor: • What do you notice about the voltage sum? Voltages across resistors in series add to make up the total voltage.

  11. Series Circuit Summary • Current is constant throughout the entire circuit. • Resistances add to give Req. • Voltages across each resistor add to give Veq.

  12. 20A 20A 20 A Devices that Make Use of the Series Configuration • Although not practical in every application, the series connection is crucial as a part of most electrical apparatuses. • Switches • Necessary to open and close entire circuits. • Dials/Dimmers • A type of switch containing a variable resistor (potentiometer). • Breakers/Fuses • Special switches designed to shut off if current is too high, thus preventing fires. • Ammeters • Since current is constant in series, these current-measuring devices must be connected in that configuration as well.

  13. Ieq I1 Ieq I2 The Parallel Circuit (cont.) • Parallel circuits are similar to rivers with branches in them. • The current from the river divides into multiple paths. • After the paths, the water recombines into the same amount of flowing water.

  14. R1 R2 Parallel Circuit • A parallel circuit is similar to a river that branches, current can flow in multiple paths. • Once the paths end, the total flow remains the same

  15. R1 R2 Branch X X Branch The Parallel Circuit • Notice that the circuit branches out to each resistor, allowing multiple paths for current to flow. • If there are exactly two clear paths from the ends of one resistor to the ends of the other resistor. A break in one of the branches of a parallel circuit will not disable current flow in the remainder of the circuit.

  16. R1 R2 Req V V Parallel Circuit • How do we find Req a parallel circuit? Use Ohm’s law Divide both sides by Vp V R2

  17. R1 R2 Req The Parallel Circuit (cont.) • Notice how every resistor has a direct connection to the DC source. This allows the voltages to be equal across all resistors connected this way. • An equivalent resistance (Req) can also be found for parallel configurations. It is as follows:

  18. 30W 30W 60W 6V 12W 6V Sample Problem (Parallel) • A circuit is configured in parallel as shown below. • What is the equivalent resistance of the circuit?

  19. 30W 30W 60W 6V Sample Problem (Parallel) • What is the current in the entire circuit? • What is the current across each resistor? The 30W Resistors The 60W Resistor

  20. Parallel Circuit Summary • There are several facts that you must always keep in mind when solving parallel problems. • Voltage is constant throughout the entire parallel circuit. • The Inverses of the Resistances add to give the inverse of Req. • Current through each resistor adds to give Ieq. • Make use of Ohm’s Law.

  21. V Devices that Make Use of the Parallel Configuration • Although not practical or safe in every application, the parallel circuit finds definite use in some electrical apparatuses. • Electrical Outlets • Constant voltage is a must for appliances. • Light Strands • Prevents all bulbs from going out when a single one burns out. • Voltmeters • Since voltage is constant in parallel, these meters must be connected in this way.

  22. Lights demo • DC source with 3 lights in series • DC source with 3 lights in parallel • DC source with 2 lights in series 1 parallel • DC source with 1 lights in series 2 parallel

  23. R3 R4 R2 R1 Series Parallel Combination Circuits • Some circuits have series/parallel combinations • These can be reduced using equivalent resistance formulas. • Now let’s solve a problem involving this circuit.

  24. Parallel 25V Series 20W 20W 30W 10W Sample Problem (Combo) What is the equivalent resistance (Req) of the circuit? • First, we must identify the various combinations present. Series Parallel 10W 40W

  25. 25V 10W 40W Parallel 25V Series Series 20W 20W 30W 10W Sample Problem (Combo) • The simplified circuit only shows the equivalent resistances. Is the circuit now fully simplified? • Now, we must identify the final configuration. 50W 10W 40W

  26. 25V 10W 40W 25V 50W Series 50W Sample Problem (Combo) • The circuit is further simplified below. Can it be simplified again? • Now, the circuit is completely simplified. • What is the current in the entire circuit?

  27. Combination Circuits • Parallel Paths: Must make a complete loop through two resistors with out touching any other component. • Series Paths: Must form a path through multiple resistors with out crossing an intersection.

  28. I1 I3 I2 • Choose a direction and label the current in each branch • Identity the number of unknowns as develop as many equation • Label the polarity of each Vr for all resistors. • Apply Kirchoff’s junction rule (sum of current in equals sum of current out. • Apply Kirchoff’s loop rule. The sum of all voltages around a loop must equal zero • Solve the simultaneous equations Kichoff's current laws 10W 35V 30W 1W 10W 40V 1W

  29. 10W Kichoff's current laws 35V 30W 1W 10W 40V 1W

  30. 15V 25V 30W 30W 10W • Make a terminal voltage slide

  31. 15V 25V 30W 30W 10W

  32. 12μf 24μf 36μf

  33. 113W 77W 151W 151W 131W 131W 130W 130W W W 117 117 120W 120W W W 114 114 140 W 220V 220V 107W 107W 126W 126W 113W 44W 44W 77W 26W 26W

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