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Intro to circuits

Intro to circuits. Moving from water to actual electrons. Review of Concepts - Current. Current is the amount of charge passing a point in the circuit in a certain length of time. Current is measured in Amperes (A). Symbol for charge is q Symbol for current is I. So, I = Δ q/ Δ t

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Intro to circuits

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  1. Intro to circuits Moving from water to actual electrons

  2. Review of Concepts - Current • Current is the amount of charge passing a point in the circuit in a certain length of time. Current is measured in Amperes (A). • Symbol for charge is q • Symbol for current is I. • So, I = Δq/Δt • Note: this is NOT the same as the number of electrons passing by per unit time

  3. Competition problem #1 • Okay, we need 4 volunteers…

  4. Review of Concepts - Voltage • Voltage is the pull on the charge as it moves around the circuit. • The unfortunately named Electromotive Force (EMF) is equivalent to voltage. • It was thought at one point that there is a ‘force’ that pushes the current around the circuit. This ‘force’ is actually a voltage, not a force.

  5. A note on batteries • In a circuit diagram, the symbol for a battery is this: + - The ‘+’ means the positive terminal and the ‘-’ means the negative terminal.

  6. Standard Convention for circuits • K, so here’s the deal: • We all know that it is electrons (i.e. negative things) that flow in the circuit. • However, by convention, we talk about current flowing FROM the positive terminal TOWARDS the negative. Just go with it. + -

  7. Resistance (is futile) • Resistance is the difficulty current has in flowing through a component in a circuit • Resistance is measured in Ohms and the symbol is Ω. • The symbol for a resistor in a circuit looks like this:

  8. Quick Side Note: Resistivity • Resistivity is the how much resistance there is per unit length of a conductor. • 2 basic concepts: • The longer the conductor, the greater the resistance • The skinnier the conductor, the greater the resistance. • So a short thick copper wire has a lower resistance than a long skinny copper wire

  9. Simple DC circuit • DC means “direct current”. I will explain what this means later.

  10. And now let’s have one of you come up and explain what we just learned. • Don’t everyone jump up at once.

  11. Now that you have heard it in your own words… • It’s time for the quiz board.

  12. Ohm’s Law (the most important equation for electricity ‘n’ stuff) • Ohm’s Law: Voltage = Current X resistance • Or, more succinctly, V = IR • Really simple example: • You have a 3V battery pushing a current of 0.4A through a certain resistance. What is the resistance? • R = V/I = 3/0.4 = 7.5 ohms

  13. Voltage drop across a resistor • Remember the water lab and the upright tubes with the water in them? • The analog of water pressure was resistance. • Recall what happened when you went across resistors: the water pressure dropped. • The analog in a real circuit is that the voltage drops when current goes across a resistor.

  14. Voltage drop across a resistor 2 • So whenever you have a resistor in a circuit, voltage drops across it according to ohm’s law. • Vdrop = IR • Voltage will drop across every resistor in a circuit until there are no more resistors

  15. Equivalent resistance • One can find the equivalent resistance of the circuit by adding all the individual resistances together. • Two resistors of 6 ohms and 3 ohms have an equivalent resistance of 9 ohms. • This only works for a series circuit

  16. Series Circuit example • Consider the circuit: • Let’s say that the battery voltage = 12V • R1 = 1 ohm • R2 = 2 ohm • R3 = 3 ohm • What is the current in the circuit?

  17. Series Circuit example continued • What is the voltage drop in each resistor? • R1 = 1 ohm, I = 2A, so V = (1ohm)(2A) = 2 V • R2 = 2 ohm, I = 2A, so V = (2ohm)(2A) = 4 V • R3 = 3 ohm, I = 2A, so V = (3ohm)(2A) = 6 V • Notice that all the voltage drops add up to the original voltage of 12 V

  18. A check for understanding • Once again with the volunteers…

  19. Series vs. Parallel • A SERIES circuit is one with no branches. • All the elements are all lined up in a single sequence (hence, a series). • A PARALLEL circuit is one in which there are branches. • The current has a choice between two or more branches to take at some point in the circuit.

  20. Example Parallel Circuit • Examine a parallel circuit:

  21. Equivalent resistance in a parallel circuit • The equivalent resistance of a parallel circuit is given by: 1/Req = 1/R1 + 1/R2 + …

  22. Let’s look at an example • If R1 = 1 ohms and R2 = 2 ohms and R3 = 3 ohms, what is the equivalent resistance? • 1/Req = 1/1 + ½ + 1/3 • 1/Req = 6/6 + 3/6 + 2/6 = 11/6 • 1/Req = 11/6, so Req = 6/11 ohms

  23. Circuits partially in series and partially in parallel • Look at the circuit below. Oh, whatever shall we do to analyze it? • Start by grouping resistors together and finding the equivalent resistances. 110Ω 220Ω 24V 180Ω 250Ω

  24. Circuits partially in series and partially in parallel continued • So resolve the two in series on the right first. 110Ω 110Ω 220Ω 24V 24V 470Ω 180Ω 180Ω 250Ω

  25. Circuits partially in series and partially in parallel continued • Now resolve the two resistors in parallel on the right, etc. • What is the final equivalent resistance in the circuit? What is the total current coming out of the battery? 110Ω 110Ω 24V 470Ω 24V 180Ω 130Ω

  26. A check for understanding • Once again with the volunteers…

  27. Kirchoff’s Laws • There are two laws that will help you analyze complex circuits and determine currents and voltages: • Kirchoff’s Junction Law • Kirchoff’s Loop Law • Let’s look at these individually

  28. Kirchoff’s Junction Law • Kirchoff’s Junction law states that the sum of currents entering into a junction has to equal the sum of the currents leaving the junction. • Look at the examples below. What can we say about the currents in the branches? Branch B I = 8amps Branch A I = 7amps Branch B I = 2amps Branch A I = 6amps Branch C I = ? Branch D I = ? Branch C I = ?

  29. Kirchoff’s Loop Law • Kirchoff’s Loop law states that the sum of voltage increases and drops around a closed loop in a circuit equals zero. • We have seen a glimpse of this rule when we began analyzing circuits. • Remember this example? • Consider the circuit: • Let’s say that the battery voltage = 12V • R1 = 1 ohm • R2 = 2 ohm • R3 = 3 ohm • What is the current in the circuit?

  30. Kirchoff’s Loop Law • In that example, the sum of the voltage increases and decreases in the loop equaled zero. • Use this idea to find the voltage drop in the resistor in the bottom right corner: 5Ω 12V + - 15V + - 6Ω

  31. Kirchoff’s Loop Law • There are two voltage rises: 12 V and 15 V • There are two voltage drops: I*(5Ω) and I*(6Ω) • The total voltage around the circuit has to equal zero • So 12V + 15V – I(5Ω) – I (6Ω) = 0 • 27V – I (11 Ω) = 0 • I = 27/11 amps = 2.45 amps • Voltage drop across bottom right resistor: V = IR • So V = (2.45amps)(6 Ω) = 14.7 V

  32. Check for Understanding • Once again with the volunteers

  33. Electrical Power • Power is given as: Power = current * voltage • P = IV • But, V = IR, so also Power = I2R • Example: Let’s say you have a standard light bulb that has a resistance of 50 Ω. A current of 1.25 amps is going through the bulb. What is the power consumption?

  34. Measuring Current • When measuring current, you want ALL the current to go through the meter.

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