chapter26 - Electric circuit components Capacitor stores...

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Electric circuit components Capacitor – stores charge and potential energy, measured in Farads (F) Battery – generates a constant electrical potential difference ( V) across it. Measured in Volts (V). Resistor – resists flow of charge due to scattering; dissipates energy. Measured in Ohms ( ) Direct Current (DC) circuits First, we will consider circuits with batteries and resistors. R V=5V I
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Resistors in Series I I I I = = = 3 2 1 3 3 2 2 1 1 IR V V IR V V IR V V yb xy ax = = = = = = ( ) 3 2 1 3 2 1 R R R I V V V V ab + + = + + = The current through all resistors is the same 3 2 1 R R R R IR V eq eq ab + + = = Resistors in Series = i i eq R R Adding resistors in series always increases the total resistance.
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Resistors in Series: Example Calculate I and V across each resistor V R A R B I bat I A I B R A = 1.0 R B = 3.0 V = 6 Volts V R A R B I bat I A I B Two different wires are connected to a battery in series (in a chain, one after another). How does the current in upper wire A compare to the current in lower wire B? A) i A > i B B) i A < i B C) i A = i B D) Impossible to determine. Clicker Question
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What is the equivalent resistance? = + = + = 0 . 4 0 . 3 0 . 1 2 1 R R R eq What is the current through the circuit? Assuming everything is Ohmic, V=IR A V R V i i i eq B A 5 . 1 0 . 4 6 = = = = = V R A R B I bat I A I B Resistors in Series: Example What about the Voltage change across each resistor? V R A R B I bat I A I B R A = 1.0 Ω, i A =1.5 A =1.5 A R B = 3.0 Ω, i B = 1.5 A V = 6 Volts V A R i V V A A A A 5 . 1 ) 0 . 1 )( 5 . 1 ( = = = = V A R i V V B B B B 5 . 4 ) 0 . 3 )( 5 . 1 ( = = = = Resistors in Series: Example
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V R A R B I bat I A I B Clicker Question If we consider the Voltage change starting at Point P and going all the way around the circuit loop back to Point P, what is the total V? Α)∆ V = +6.0 Volts Β)∆ V = +1.5 Volts C) V = -4.5 Volts D) V = 0.0 Volts E) V = -6.0 Volts Point P V R A R B I bat I A I B P1 P2 P3 P4 P5 Position In Loop Voltage 1 2 3 4 5 1 6V 4.5V 3.0V 1.5V 0.0V Define V=0 at P1. Resistors in Series: Example
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Clicker Question We start with the left circuit with one lightbulb (A). The brightness of the bulb directly reflects the power. If we add a second bulb (B) as shown on the right, what happens to the bulbs? V A V A B A)Bulb A is equally bright. B)Bulb A is dimmer than before C)Bulb A is brighter than before Two light bulbs, A and B, are in series, so they carry the same current. Light bulb A is brighter than B. Which bulb has higher resistance? A) A B) B C) Same resistance. V A B Answer: Bulb A has higher resistance. Since the resistors are in series, they have the same current I. According to P = I 2 R, if I = constant, then higher R gives higher P.
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