Phys 102 – Lecture 7 Series and parallel circuits 1

Today we will... Phys. 102, Lecture 7, Slide 2 ++ Learn about electric circuits Circuits with a battery, wires, and resistors Circuits with a battery, wires, and capacitors Analyze circuits Take a complex-looking circuit like......and turn into a simple-looking circuit like

Recall from last time... Phys. 102, Lecture 7, Slide 3 Electric potential difference across circuit element is its “voltage” V element Should be “ΔV”, but we’ll usually drop the “Δ” Resistors – regulate current Dissipate power R Capacitors – store charge Store energy C + Batteries – pump charges Provide emf for charges ε Circuits connect elements with wires, which we treat as ideal conductors

Kirchhoff loop rule Phys. 102, Lecture 7, Slide 4 + A charge making a complete loop around a circuit must return to the same electric potential (“height”) at which it started Battery (pump) Resistor R (bumpy hill) + ε VRVR Sum of electric potential differences (voltages) around circuit loop is zero ε R

Series components Phys. 102, Lecture 7, Slide 5 Two components are said to be in series when they are connected end-to-end by a single wire V1V1 ε V2V2 + ε R1R1 R2R2 R1R1 R2R2 I1I1 I2I2

A. V 1 > V 2 B. V 1 = V 2 C. V 1 < V 2 ACT: CheckPoint R 1 = 1 Ω R 2 = 10 Ω ε Consider a circuit with two resistors R 1 and R 2 in series. Compare the voltages across the resistors:

ACT: Capacitors in series Phys. 102, Lecture 7, Slide 7 + ε Consider a circuit with two capacitors C 1 and C 2 in series. Compare the voltages across the capacitors: A. V 1 > V 2 B. V 1 = V 2 C. V 1 < V 2 C 1 = 1 μF C 2 = 10 μF

Equivalent resistance & capacitance Phys. 102, Lecture 7, Slide 8 Circuit behaves the same as if series components were replaced by a single, equivalent component R1R1 R2R2 ResistorsCapacitors == R eq C1C1 C2C2 C eq V1V1 V2V2 V eq V1V1 V2V2 I eq I2I2 I1I1 Q1Q1 –Q 1 Q2Q2 –Q 2 Q eq –Q eq

Calculation: vascular resistance Phys. 102, Lecture 7, Slide 9 Pressure difference Blood flow Vascular resistance emf Electric current Electrical resistance The circulatory system is analogous to an electric circuit The circulatory system consists of different types of vessels in series with different resistances to flow *Numbers represent accurate relative values ArteryArterioleCapillaryVenuleVein ε heart = 120 V* R A = 20 ΩR a = 50 ΩR c = 20 ΩR v = 6 ΩR V = 4 Ω

Calculation: vascular resistance Phys. 102, Lecture 7, Slide 10 ε heart = 120 V R A = 20 ΩR a = 50 ΩR c = 20 ΩR v = 6 Ω Calculate the current I through the vascular circuit and the voltages across the different types of vessels R V = 4 Ω ArteryArterioleCapillaryVenuleVein Simplify ε heart R eq Expand

Kirchhoff junction rule – Junction Phys. 102, Lecture 7, Slide 11 Charges flowing through a junction split. By conservation of charge, the sum of currents into a junction equals the sum of currents out of a junction I3I3 I2I2 I1I1 I1I1 I2I2 I3I3

Parallel components Phys. 102, Lecture 7, Slide 12 ε V1V1 V2V2 Components are said to be in parallel when both ends are connected to each other, forming a loop containing only them + ε R1R1 R2R2 I2I2 I1I1 I I1I1 II2I2

ACT: Parallel or series? Phys. 102, Lecture 7, Slide 13 + Consider the circuit to the right. Which of the following statements is true? A. C 1 & C 4 are in series B. C 2 & C 4 are in parallel C. C 1 & C 3 are in parallel ε C2C2 C4C4 C1C1 C3C3

R 1 = 1 Ω ACT: Resistors in parallel + Consider a circuit with two resistors R 1 and R 2 in parallel. Compare I 1, the current through R 1, to I 2, the current through R 2 : R 2 = 10 Ωε A. I 1 > I 2 B. I 1 = I 2 C. I 1 < I 2 Phys. 102, Lecture 7, Slide 14

ACT: CheckPoint 2.3 R1R1 + R2R2 ε Now we add a switch S. What happens to the current out of the battery when the switch is closed? A. I battery increases B. I battery remains the same C. I battery decreases DEMO S Phys. 102, Lecture 7, Slide 15

Equivalent resistance & capacitance Phys. 102, Lecture 7, Slide 16 Circuit behaves the same as if parallel components were replaced by a single, equivalent component R1R1 R2R2 Resistors Capacitors == R eq C1C1 C2C2 C eq V1V1 V2V2 V eq V1V1 V2V2 I eq I2I2 I1I1 Q1Q1 –Q 1 Q2Q2 –Q 2 Q eq –Q eq

Calculation: vascular resistance Phys. 102, Lecture 7, Slide 17 In previous calculation, capillaric resistance accounts for ~20% of total vascular resistance, yet capillaries are the thinnest blood vessels, and should have the highest resistance. Why? Artery Capillary Venule Vein Arteriole

Calculation: cardiovascular system Phys. 102, Lecture 7, Slide 18 R brain R pulm R body ε heart + The human cardiovascular system consists of two circuits: pulmonary circulation which carries blood though the lungs, and systemic circulation which carries blood to the organs Calculate current through each component of circulatory system R pulm = 12 Ω, R brain = 1 kΩ, R body = 160 Ω, ε heart = 120 V The organs of the body are connected in parallel in the systemic circuit Simple circuit model*: *Numbers represent accurate relative values

ACT: analyzing circuits Phys. 102, Lecture 7, Slide 19 Which of the following circuit is different than the others? IIIIII A. Circuit I B. Circuit II C. Circuit III D. All three are equivalent E. All three are different + + +

Calculation: circulatory system Phys. 102, Lecture 7, Slide 20 + R pulm = 12 Ω, R brain = 1 kΩ, R body = 160 Ω, ε heart = 120 V Calculate current through each component of circulatory system R brain & R body are in parallelR pulm & R syst are in series Simplify R brain R pulm R body ε heart + R pulm R syst ε heart + R tot ε heart

Calculation: circulatory system Phys. 102, Lecture 7, Slide 21 + Expand R pulm & R syst are in series R pulm = 12 Ω, R brain = 1 kΩ, R body = 160 Ω, ε heart = 120 V Calculate current through each component of circulatory system R tot ε heart + R pulm R syst ε heart

Calculation: circulatory system Phys. 102, Lecture 7, Slide 22 + Expand R brain & R body are in parallel R pulm = 12 Ω, R brain = 1 kΩ, R body = 160 Ω, ε heart = 120 V Calculate current through each component of circulatory system R tot ε heart + R pulm R syst ε heart + R brain R pulm R body ε heart

Summary of today’s lecture Two basic principles: Kirchhoff loop rule Voltages around circuit loop sum to zero (based on conservation of energy) Kirchhoff junction rule Currents into a circuit branch equal currents out (based on conservation of charge) Phys. 102, Lecture 7, Slide 23

Summary of today’s lecture Series components Currents are the same Voltages add ResistorsCapacitors Parallel components Voltages are the same Currents add ResistorsCapacitors Don’t mix equations! Phys. 102, Lecture 7, Slide 24