Download 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 = 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)
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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.
110Ω
220Ω
24V
180Ω
250Ω
Circuits partially in series and
partially in parallel continued
• So resolve the two in series on the right
first.
110Ω
110Ω
220Ω
24V
24V
180Ω
250Ω
180Ω
470Ω
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
24V
180Ω
110Ω
470Ω
24V
130Ω
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 A
I = 7amps
Branch B
I = 2amps
Branch C
I=?
Branch A
I = 6amps
Branch C
I=?
Branch B
I = 8amps
Branch D
I=?
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?
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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
12V
+
-
-
6Ω
+
15V
Kirchoff’s Loop Law
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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
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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.