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18 Overview

• resistor & capacitor circuits

• Kirchoff’s Rules

• voltmeters & ammeters

• household circuits & safety

• Homework:

• 17, 27, 31, 33, 55, 67, 71, 85

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Connection Types

______

______l

3

junctions & loops

• Current value ______________ at __________________.

• Ex. Point b is a junction

• A closed path is called a ___________

• Ex. bcdeb

4

Equivalent Resistance

• The ______________ of a network of resistors is called the _____________________.

• The equivalent circuit is the circuit made by replacing the network with an equivalent resistance valued resistor.

5

Resistors in Series

21 RRReq

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Resistors in Parallel

112

11

RRReq

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What happens to the equivalent resistance of a series network as more resistors are

added to it?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45

1. increases

2. decreases

3. stays same

4. cannot be determined

8

What happens to the equivalent resistance of a parallel network as more resistors are

added to it?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45

1. increases

2. decreases

3. stays same

4. cannot be determined

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Ex. Find a) equivalent resistance of the circuit. B) the current in and voltage across each resistor , c) the power dissipated by each resistor.

106421 RRReq

AVRVI eqeq 2.110/12

AIII eq 2.164

VARIV 8.4)4)(2.1(44

VARIV 2.7)6)(2.1(66 WARIP 76.5)4()2.1()( 22

44

WARIP 64.8)6()2.1()( 2266

10

Ex. Find a) equivalent resistance of the circuit, b) the current in and voltage across each resistor , c) the power dissipated by each resistor.

4.264

111112

11 RRReq

AVRVI eqeq 0.54.2/12

VVV 1264

AVRVI 0.34/1244 AVRVI 0.26/1266

WARIP 36)4()0.3()( 2244

WARIP 24)6()0.2()( 2266

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Calculate the equivalent resistance:

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Kirchoff’s 1st Rule• 1) current into junction = current out

• Ex. I = I1+I2 __________________

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Kirchoff’s 2nd Rule

• 2) voltage change around any loop is ____

• Ex. -I2(6)+I1(4) = 0

• _________________________

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Measuring Devices

• become __________of the circuit being measured

• each device has ________________

• (ideally) the meter’s resistance should ____________ the resistance of the circuit

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Voltmeters

• used in ____________ with a circuit element (circled V in diagram)

• (ideally) the voltmeter should have ____________ internal resistance

• /

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Ammeters

• used in __________ (circled A in diagram)

• (ideally) the ammeter should have ______ internal resistance

• /

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RC Circuits

• any circuit with a resistor and a capacitor

• Time constant = RC

• s = ·F

• Ex. 50ohm, 2F

• RC = 100s

• /

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Charging a Capacitor

)1( /RCtC eVV

V

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Ex. R=100, C=0.5, V = 6.0

• How long for capacitor to get to 4.0 volts?

• RC = (100)(0.5) = 50 seconds

• Equation:

• solve for t:

)1(0.6 50/tC eV

)1(0.60.4 50/te50/167.0 te

33.050/ te

)33.0ln()ln( 50/ te

1.150/ t

st 55)1.1(50

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Discharging a Capacitor

RCtoC eVV /

RCto eR

VI /

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Ex. R=80, C=1.0, Vo = 5.0

• How long for capacitor to get to 3.5 volts?

• RC = (80)(1) = 80 seconds

• Equation:

• solve for t:

80// 0.5 tRCtoC eeVV

80/0.55.3 te80/0.55.3 te

7.00.5/5.380/ te

36.080/ t st 8.28)36.0(80

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Household Circuits

• US: _________ @ _____________

• Europe, etc.: 220 @ ______ hertz

• ground wires allow excess current to go into the ground (safety feature).

• circuit breakers & fuses stop the current flow if it passes a certain value (safety).

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Summary

• series & parallel circuit analysis

• junctions, loops & Kirchoff’s Rules

• RC circuits

• voltmeters & ammeters

• household circuits & safety