Electrical Circuits They keep the lights on!!

Electrical Current is how fast charge is moving in a unit of time. I is current. Current is measured in amperes or amps (A).

Remember it is charge that is moving! Electrons move very little!!

Physics knows its electron flow but often use conventional current.

Direction of the current is taken to be opposite of the electron motion.

Ohm’s Law is that different metals have different resistance to electrical flow independent of Voltage. V = IR V is voltage or how much electricity (how much “push”) and is measured in Volts (V) I is current and is measured in Amps (A) R is resistance to current and is measured in Ohms (Ω)

Voltage is called “potential difference” and change in Voltage is called “drops”.

This means you have “more” charge in one area and “less” charge in another!

potential difference = drop There must be a potential drop from one end to another to have current. potential difference = drop V = IR V is created by having more electrical charge at one end and less electrical charge at another end.

Deviation from Ohm’s Law Not all materials obey Ohm’s Law. The filament of a light bulb has increasing resistance as current increases. It only obeys Ohm’s Law at low temperatures.

Resistance slows electricity down as it moves through a circuit Resistance slows electricity down as it moves through a circuit. It has a symbol of R and is measured in Ohms (Ω).

Factors Affecting Resistance R is directly proportional to length of the wire. The longer the wire the more resistance. R is inversely proportional to cross-sectional area of the wire. The “thicker” the wire the less resistance. R is directly proportional to temperature. The higher the temperature in the wire the more resistance.

Electrical Power Either thermal energy or work done by an electrical device. These equations come in handy!!

Electrical Power If any two of voltage, current, and resistance are known then power can be calculated. P = V I P = R I2 V2 P = R

Electricity and Circuits Property Units of Measure Voltage (V) Current (I ) Resistance (R) Power (P) Volts (V) Amps (A) Ohms (Ω) Watts (W)

Here are examples of both a series and parallel circuit. Simple Circuits Here are examples of both a series and parallel circuit.

Simple Circuits The left circuit is in series, if one bulb goes out the entire circuit is disrupted.

Simple Circuits The right circuit is in parallel. If one bulb goes out the other will remain on.

Simple Circuits All circuits must be complete from the positive to negative terminal of the battery.

Symbols in Circuit Diagrams! Battery Conductor Switch Light Bulb or Lamp Resistors

Resistance in Series R1 R2 R3 24 V 0 V I Rtotal = R1 + R2 + R3

Resistance on the circuit is the sum of the individual resistors Rtotal = R1 + R2 + R3

Resistance on the circuit is the sum of the individual resistors 2Ω 4Ω 5Ω 24 V 0 V I Rtotal = 2Ω + 4Ω + 5Ω = 11Ω

Current on the circuit follows Ohm’s Law 2Ω 4Ω 5Ω 24 V 0 V I V = IR

Current on the circuit follows Ohm’s Law 2Ω 4Ω 5Ω 24 V 0 V I 24V = I 11Ω

Current on the circuit follows Ohm’s Law 2Ω 4Ω 5Ω 24 V 0 V I I = 2.2A

This is true across any resistor as well. = 2Ω 4Ω 5Ω 24 V 0 V I V = 2.2A 2Ω

There is a 4.4V drop at the first resistor. = 2Ω 4Ω 5Ω 24 V 0 V I V = 4.4V

At point A the voltage has dropped. = 2Ω 4Ω 5Ω A 24 V 0 V I 24V - 4.4V = 19.6V

Resistance in Parallel 24 V 0 V I 1 1 1 1 = + + Rtotal R1 R2 R3

Resistance in Parallel 24 V 0 V I R1= 2Ω 1 1 1 1 R2= 4Ω = + + Rtotal R1 R2 R3 R3= 5Ω

Resistance in Parallel 24 V 0 V I R1= 2Ω 1 1 1 1 R2= 4Ω = + + Rtotal 2Ω 4Ω 5Ω R3= 5Ω

Resistance in Parallel 24 V 0 V I R1= 2Ω 1 R2= 4Ω = + 0.5 + 0.25 0.2 Rtotal R3= 5Ω

Resistance in Parallel 24 V 0 V I R1= 2Ω 1 R2= 4Ω = 0.95 Rtotal R3= 5Ω

Resistance in Parallel 24 V 0 V I R1= 2Ω R2= 4Ω Rtotal = 1.05 Ω R3= 5Ω

Resistance in Parallel 24 V 0 V I Remember the Golden Rule: In parallel resistors resistance on the system must be less than that of the lowest resistor!

R3 R2 R1 24 V 0 V I R1= 2Ω This is due to the property current has to take the path of least resistance R2= 4Ω R3= 5Ω

Voltage across parallel lines is always the same! 2Ω I 4Ω 5Ω 2 A Voltage across parallel lines is always the same! The resistance of this parallel system is 1.05 Ω

The voltage drop can be found using V = IR 2Ω I 4Ω 5Ω 2 A The voltage drop can be found using V = IR V = (2 A)(1.05 Ω) V = 2.1V When we learn current splits we will discover it is the same drop for each resistor individually!

The Voltage through the 4Ω and 8Ω resistors are the same! Rules to Remember In a parallel circuit system, the voltage is the same in all parallel paths. The Voltage through the 4Ω and 8Ω resistors are the same!

The Voltage through the 4Ω and 8Ω resistors are the same! Rules to Remember It helps to think of Voltage as the “push” through a circuit, like an invisible hand pushing charge along. The Voltage through the 4Ω and 8Ω resistors are the same!

Rules to Remember To find current on the circuit the resistance across the entire circuit must be known as well as voltage out of the battery. The Resistance is 3+10+5 = 18Ω The Current is V = IR 9V = I 18Ω I = 0.5 A

The Voltage is 9V at point 1 and 7.5V at point 2. Rules to Remember In a series circuit system, the voltage drops as current goes through each resistor. The Voltage is 9V at point 1 and 7.5V at point 2. V = IR V = (0.5A)(3Ω) V = 1.5V

The Voltage is 7.5V at point 2 and 2.5V at point 3. Rules to Remember In a series circuit system, the voltage drops as current goes through each resistor. The Voltage is 7.5V at point 2 and 2.5V at point 3. V = IR V = (0.5A)(10Ω) V = 5V

The Voltage is 2.5V at point 3 and 0 at point 4. Rules to Remember In a series circuit system, the voltage drops as current goes through each resistor. The Voltage is 2.5V at point 3 and 0 at point 4. V = IR V = (0.5A)(5Ω) V = 2.5V

The Voltage is 2.5V at point 3 and 0 at point 4. Rules to Remember To understand this it helps to think of voltage as “push”. Some of this “push” is used up as each resistor system is crossed. The Voltage is 2.5V at point 3 and 0 at point 4. V = IR V = (0.5A)(5Ω) V = 2.5V

Rules to Remember In a parallel circuit system, the current splits as it enters and comes back together as it exits. The Current through the 4Ω and 8Ω resistors are the same going in and out!

Rules to Remember Current is always the “same in, same out” More Current goes through the 4Ω resistor than the 8Ω resistor!

Rules to Remember The 0.5 A will be split between the 4Ω and 8Ω resistors!!! 8/12 of the Current goes through the 4Ω resistor! 0.5A (8/12) = 0.33 A

Rules to Remember The 0.5 A will be split between the 4Ω and 8Ω resistors!!! 4/12 of the Current goes through the 8Ω resistor! 0.5A (4/12) = 0.17 A

Rules to Remember The current comes back together after going through the resistors! The Current to the battery! 0.33A + 0.17A = 0.5 A

Rules to Remember When you have parallel systems mixed with resistors in series, solve for the resistance of the parallel system and then treat it as part of the series. It is very common to have series and parallel resistors mixed together on a circuit.

Example 2Ω 4Ω 3Ω 6Ω 2Ω The 4Ω, 3Ω, 6Ω resistors are a parallel system in series with the other resistors!!

First solve for the total resistance of the parallel system!! Example 2Ω 4Ω 3Ω 6Ω 2Ω First solve for the total resistance of the parallel system!!

Example 2Ω 4Ω 3Ω 6Ω 2Ω 1 1 1 1 = + + Rtotal 4 3 6

Example 2Ω 4Ω 3Ω 6Ω 2Ω 1 3 4 2 9 = + + = Rtotal 12 12 12 12

Example 2Ω 4Ω 3Ω 6Ω 2Ω 1 9 12 = Rtotal = = 1.33Ω Rtotal 12 9

Now add the resistance of the parallel system to the series!!! Example 2Ω 4Ω 3Ω 6Ω 2Ω Now add the resistance of the parallel system to the series!!!

Example 2Ω 4Ω 3Ω 6Ω 2Ω 2Ω + 1.33Ω + 2Ω = 5.33Ω

Current in Parallel

In is the current across the individual resistor. Rtotal In = Itotal Rn In is the current across the individual resistor. Itotal is the total current entering the parallel system. Rtotal is the total resistance of the parallel system. Rn is the resistance of the individual resistor.

Example of Parallel Current 4Ω I = 6A I = 6A 6Ω 8Ω 1 1 1 1 = + + Rtotal 4Ω 6Ω 8Ω

Example of Parallel Current 4Ω I = 6A I = 6A 6Ω 8Ω 1 6 4 3 13 = + + = Rtotal 24 24 24 24

Example of Parallel Current 4Ω I = 6A I = 6A 6Ω 8Ω 24 Rtotal = = 1.85Ω 13 Now we can solve for the current through each resistor!

Rtotal In = Itotal Rn 1.85Ω I4 = 6A 4Ω I4 = 2.77A

Rtotal In = Itotal Rn 1.85Ω I6 = 6A 6Ω I6 = 1.85A

Rtotal In = Itotal Rn 1.85Ω I8 = 6A 8Ω I8 = 1.38A

Example of Parallel Current 4Ω I = 6A I = 6A 1.85A 6Ω 1.38A 8Ω = 2.77A + 1.85A + 1.38A 6A

Ammeters They are built into circuits to give the current level at that point. They have as little resistance as possible. Ammeters are put in series so they do not change the current of the circuit Remember current splits in parallel!!!

Galvanometers read current through magnetic fields and are obsolete.

Voltmeters Voltmeters are built into circuits and give voltage at that point. They are very good for giving the “voltage drop” of a particular device. Voltmeters are put in parallel to the devices they read. Remember the voltage across any two parallel lines are the same!

Digital Multimeters They can read voltage, current, resistance, and even temperature. They range from less than $10 to hundreds of dollars. They are making ammeters and voltmeters obsolete!!

Fuses A fuse is designed to melt and disrupt or break a circuit before current levels get dangerous. This is why computers and LCD televisions should be plugged into a “surge protector” instead of straight into a wall. Modern electronics need more protection from temporarily high current levels or “surges”.

Fuses A fuse is rated by the amp level at which it melts, such as a 10 amp fuse. The power of devices is rated at a specific voltage level. A 300 W device at 110 V will have a different power at a different voltage.

Calculating Power

Calculating Power When using the P = VI equation the voltage used is the “voltage drop” or push “used up” at that particular resistor. The current used is the current through the resistor. Same with resistance, the Ω value of that resistor. Only exception is when asked the power on the circuit.

What is the resistance of the two 4Ω in parallel? A Power Example 4Ω 4Ω 2Ω 20 V 0 V I What is the resistance of the two 4Ω in parallel? Rp = 2Ω

What is the resistance on the circuit? A Power Example 4Ω 4Ω 2Ω 20 V 0 V I What is the resistance on the circuit? Rt = 4Ω

What is the current on the circuit? A Power Example 4Ω 4Ω 2Ω 20 V 0 V I What is the current on the circuit? I = 5A

What is the voltage drop on the 2Ω resistors? A Power Example 4Ω 4Ω 2Ω 20 V 0 V I = 5A What is the voltage drop on the 2Ω resistors? V = 10V

What is the voltage drop on the parallel 4Ω resistors? A Power Example 4Ω 4Ω 2Ω V = 10V 20 V 0 V I = 5A What is the voltage drop on the parallel 4Ω resistors? V = 10V

What is the current on the 2Ω resistor? A Power Example 4Ω 5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A What is the current on the 2Ω resistor?

What is the current on the parallel 4Ω resistors? A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A What is the current on the parallel 4Ω resistors?

Now calculate Power using P = VI A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A Now calculate Power using P = VI P for 2Ω = 10V 5A = 50W

Now calculate Power using P = VI A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A Now calculate Power using P = VI P for 4Ω = 10V 2.5A = 25W

Now calculate Power using P = RI2 A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A Now calculate Power using P = RI2 P for 2Ω = 2Ω (52)A = 50W

Now calculate Power using P = RI2 A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A Now calculate Power using P = RI2 P for 4Ω = 4Ω (2.52)A = 25W

Now calculate Power using P = (V2) /R A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A Now calculate Power using P = (V2) /R P for 2Ω = (102)V / 2Ω = 50W

Now calculate Power using P = (V2) /R A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A Now calculate Power using P = (V2) /R P for 4Ω = (102)V / 4Ω = 25W

See how they are all the same? A Power Example 2.5A 4Ω 5A 2.5A 4Ω V = 10V 2Ω V = 10V 20 V 0 V I = 5A See how they are all the same?

Resistance can be found with the equation Power Changes An electrical device is rated at 500 W at 220 V. What will the power of the device be if it is switched to a 110 V power source? Assume that its resistance is not variable. Resistance can be found with the equation P = V2/R. 500W = 2202V/R. R= 48400V/500W. R= 96.8Ω.

Current can be found with the equation Power Changes Now we need to find the current when the device is plugged in to the 110V source. Current can be found with the equation V = I R. 110V = I 96.8Ω. I = 110V / 96.8Ω I = 1.14A.

Power Changes Now we can find the power of the device plugged into the 110V outlet. Current can be found with the equation P = V I P = 110V 1.14A P = 125W

The End