Download presentation

Presentation is loading. Please wait.

Published byElizabeth Donahue Modified over 6 years ago

2
Topic 5.2 Extended A – Resistances in series and parallel The easiest way to picture a resistor is as a road construction zone in a highway: Here is the highway, supporting the maximum traffic flow. Here is the construction zone, constricting the flow of traffic: Of course, what will really happen is that the blocked lane of traffic will merge with the moving one. Cutting the speed by about a factor of two. NOTE: If instead of a two lane highway you had a three lane highway, a roadblock in one lane would slow the traffic by about a third. A roadblock in two lanes would slow the traffic by about two thirds. FYI: The roadblocks are one after the other, AKA INLINE. We say that they are in series.

3
Now imagine two parallel two-lane highways: Each highway begins by supporting the original flow of traffic from the previous slide. Topic 5.2 Extended A – Resistances in series and parallel Each highway has its traffic flow cut in half. But there are TWO highways. FYI: The roadblocks are in parallel. Thus the traffic flow is equivalent to a single unblocked highway.

4
Topic 5.2 Extended A – Resistances in series and parallel We can think of resistances in series in another way: Placing resistors in series increases the EFFECTIVE LENGTH of the resistor. L L L 3L SERIES R L Placing resistors in parallel increases the EFFECTIVE AREA of the resistor. A A A PARALLEL R 1 / A 3A FYI: Combining two or more resistors is series produces a resistance that is larger than any single resistor. FYI: Combining two or more resistors is parallel produces a resistance that is smaller than any single resistor.

5
Now for some formulas... Consider three resistors in SERIES, as shown: Topic 5.2 Extended A – Resistances in series and parallel + - SERIES R1R1 R2R2 R3R3 V1V1 V2V2 V3V3 Note that the current I is the same everywhere. Recall that the sum of the voltages in a loop equals the terminal voltage of the battery: Thus V V = V 1 + V 2 + V 3 = IR 1 + IR 2 + IR 3 = I(R 1 + R 2 + R 3 ) = IR s where R s is the equivalent series resistance. R s = R 1 + R 2 + R 3 Equivalent Series Resistance R s

6
Consider three resistors in PARALLEL, as shown: Topic 5.2 Extended A – Resistances in series and parallel + - PARALLEL R1R1 R2R2 R3R3 A1A1 Note that the voltage V is the same everywhere. Because of the conservation of charge, the sum of the currents going through the resistors must equal the total current: V V = V 1 = V 2 = V 3 VRpVRp Equivalent Parallel Resistance R p A2A2 A3A3 ApAp I1I1 I2I2 I3I3 I I = I 1 + I 2 + I 3 From Ohm's law, = + + V1R1V1R1 V2R2V2R2 V3R3V3R3 VRpVRp VR1VR1 VR2VR2 VR3VR3 1Rp1Rp 1R11R1 1R21R2 1R31R3

7
Find the equivalent resistance (from A to B) of the following resistor setup: Topic 5.2 Extended A – Resistances in series and parallel The resistors are in SERIES so that 25 50 100 R s = R 1 + R 2 + R 3 R s = 25 + 50 + 100 R s = 175 A B

8
Find the equivalent resistance of the following resistor setup: Topic 5.2 Extended A – Resistances in series and parallel The resistors are in PARALLEL so that 25 50 100 A B 1Rp1Rp = + + 1R11R1 1R21R2 1R31R3 1Rp1Rp 1 50 1 25 1 100 1Rp1Rp = + + 2 100 4 100 1 100 1Rp1Rp = 7 100 R p = 14.28

9
Find the equivalent resis- tance of the following resistor setup: Topic 5.2 Extended A – Resistances in series and parallel Two resistors are in PARALLEL so that 25 50 100 A B 1Rp1Rp = + 1R11R1 1R21R2 1Rp1Rp = 5 100 R p = 20 1Rp1Rp = + 1 25 1 100 4444 20 50 A B REDUCED FORM The resistors are in SERIES: R s = R 1 + R 2 R s = 50 + 20 R s = 70

10
The current through the circuit with three resistors in SERIES... Topic 5.2 Extended A – Resistances in series and parallel + -...will stop if any one resistor is removed. + - A1A1 A2A2 A3A3 ApAp The current through the circuit with three resistors in PARALLEL... Will NOT stop if any one resistor is removed.

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google