Resistors in Parallel and Series

Resistors https://commons.wikimedia.org/wiki/File:Electronic-Axial-Lead-Resistors-Array.jpg https://commons.wikimedia.org/wiki/File:Carbon_and_ceramic_resistors_of_different_power_ratings.jpg

Resistor Symbol The symbol for a resistor in circuit diagrams.

Parallel Resistors Resistors are connected in parallel when the ends of the resistors are connected directly together. Notice that in this example the ends of the resistors are connected directly to the terminals of the battery, so the resistors have the same voltage applied to them. While not all parallel resistors are connected directly to the battery, all resistors connected in parallel have the same voltage across them.

Series Resistors Series resistors are connected end to end so that they form a chain. Notice that there is only one path through the series resistors. This means that series resistors have the same current flowing through them.

Parallel Independent If one of the resistors is removed from a parallel connection, current will still flow through the other resistor. This means the parallel resistors are independent of each other. A real life example of this found in house wiring – if one light in a room is turned off, other lights in the room can remain on.

Series Dependent If one resistor in a series connection is removed, there is no current through the other resistor. This means the series resistors are dependent on each other. A real life example of this is a string of holiday lights where one bulb burns out and all the other bulbs also go out.

Parallel Equation Rp always less than the smallest Ri Parallel resistors are at the same voltage Parallel resistors divide current between them To find the total resistance of a parallel combination the reciprocals of the resistors are added to find the reciprocal of the total resistance. Notice that this means that the total resistance is actually less than the smallest individual resistance.

Series Equation Rs always greater than the largest Ri Series resistors have the same current Series resistors divide voltage between them To find the total resistance of series resistors the individual resistances are simply added. Notice that this results in a total resistance that is larger than the biggest individual resistance.

AP Equations Series Parallel

Equivalent Resistance

Series Connection Parallel to R1 Combination in Series with r Series Connection

Equivalent Resistance 20Ω 20Ω 30Ω 25Ω A B 60Ω What is the equivalent resistance between A and B? In other words, what is the value of a single resistor that would have the same effect as all the resistors shown? 60Ω What is the equivalent resistance between A and B?

Simplification 20Ω 20Ω 30Ω 25Ω A B 60Ω 60Ω The process of simplification is one in which section of the network are analyzed independently and then replaced with their equivalent resistance. The section outlined in red is a parallel connection, for example, so the equation for parallel connections should be applied.

20Ω 10Ω 25Ω A B 60Ω The parallel connection from the previous slide has been replaced by the equivalent resistance, simplifying the circuit. The process is then repeated.

10Ω 25Ω 15Ω B A The process is done when the network has been simplified to a single resistor. The equivalent resistance between A and B is 50Ω.

Power and Energy in Circuits

Power Other Equations For Power

The electric company measures energy in kilowatt-hours (kWh or kWhr): What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time. E=PΔt The electric company measures energy in kilowatt-hours (kWh or kWhr): 1 kWh = (1000 W)(3600 s) = 3.60 x 106 J.

Other Units Energy could also be measured in: Whr Wmin or any other combination of Power and Time

Example Calculate the resistance of a 40-W automobile headlight designed for 12 V. Copyright © 2009 Pearson Education, Inc.