intro to circuits
Post on 13-Jan-2016
14 Views
Preview:
DESCRIPTION
TRANSCRIPT
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 = Δq/Δt
• Note: this is NOT the same as the number of electrons passing by per unit time
Competition problem #1
• Okay, we need 4 volunteers…
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.
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.
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.
+ -
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:
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
Simple DC circuit
• DC means “direct current”. I will explain what this means later.
And now let’s have one of you come up and explain what we just
learned.
• Don’t everyone jump up at once.
Now that you have heard it in your own words…
• It’s time for the quiz board.
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
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.
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
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
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?
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
A check for understanding
• Once again with the volunteers…
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.
Example Parallel Circuit
• Examine a parallel circuit:
Equivalent resistance in a parallel circuit
• The equivalent resistance of a parallel circuit is given by:
1/Req = 1/R1 + 1/R2 + …
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
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.
24V
110Ω
220Ω
250Ω
180Ω
Circuits partially in series and partially in parallel continued
• So resolve the two in series on the right first.
24V
110Ω
220Ω
250Ω
180Ω
110Ω
180Ω 470Ω24V
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
180Ω 470Ω24V
110Ω
130Ω24V
A check for understanding
• Once again with the volunteers…
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
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 BI = 2amps
Branch CI = ?
Branch AI = 7amps
Branch AI = 6amps
Branch BI = 8amps
Branch CI = ?
Branch DI = ?
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?
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
6Ω
+
- +
-12V15V
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
Check for Understanding
• Once again with the volunteers
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?
Measuring Current
• When measuring current, you want ALL the current to go through the meter.
top related