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.