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PHYS 1022: Chap. 31-32, Pg 2

Topics: •  Conductivity and Resistivity •  Resistance and Ohm’s Law

•  Capacitors in series and parallel •  Resistors in series and parallel •  Kirchhoff’s Rules

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PHYS 1022: Chap. 31-32, Pg 5 New Topic

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  The electric field is directly proportional to the current density in the wire.

  ρ is called resistivity, R is the resistance  a measure of how hard a charge can move in a material

  SI unit: V.m / A = Ω. m

  A perfect conductor has zero resistivity. A perfect insulator has infinite resistivity   The reciprocal of resistivity (1/ρ) is called conductivity σ.

€

V = RI

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  The resistivity of a material depends on temperature. Metal near room temperature:

PHYS 1022: Chap. 31-32, Pg 8

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PHYS 1022: Chap. 31-32, Pg 13

Topics: •  Conductivity and Resistivity •  Resistance and Ohm’s Law

•  Capacitors in series and parallel •  Resistors in series and parallel •  Kirchhoff’s Rules

PHYS 1022: Chap. 31-32, Pg 14 New Topic

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PHYS 1022: Chap. 31-32, Pg 15

C is called an equivalent capacitor.

 Since Q = C V, we have  C1V+ C2V + C3V = CV

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1 1

1 C C 1

2 C = + 1

3 C +

 Since V = Q/C, we have  Q/C1+ Q/C2 + Q/C3 = Q/C

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PHYS 1022: Chap. 31-32, Pg 17

What is the equivalent capacitance of the combination

shown ?

o

o

C C C

Ceq

1)  3C/2 2)  2C/3 3)  3C 4)  2C 5)  C/2

PHYS 1022: Chap. 31-32, Pg 18

How does the voltage V1 across the C1 compare to the voltage

V2 across C2?

1)  V1 = V2 2)  V1 > V2 3)  V1 < V2 4)  all voltages are

zero

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PHYS 1022: Chap. 31-32, Pg 19

How does the charge Q1 across C1 compare to the charge Q2

across C2?

1)  Q1 = Q2

2)  Q1 < Q2

3)  Q1 > Q2

4)  all charges are zero

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  Find the charge, potential difference, and energy stored in each capacitor.

PHYS 1022: Chap. 31-32, Pg 22 New Topic

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PHYS 1022: Chap. 31-32, Pg 24 Req is the reciprocal of the sum of the reciprocals.

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(or: what goes in has to come out!)

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  “The sum of voltage drops and gains around any closed circuit loop must be zero”

Sign convention: – sign for voltage drop and +

sign voltage gain.

ΔV1 + ΔV2 + ΔV3 + ΔV4 + … = 0

It depends on several factors: 1.  emf or resistor

2.  direction of current 3.  direction of loop travel

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What is the current at point P?

5 A

8 A

2 A

P

1)  2 A 2)  5 A 3)  6 A 4)  10 A

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2 Ω 4 Ω

–IR = –8 V –IR = – 4 V

+ε = 12 V

Start

+ 12 V – 8 V – 4 V = 0 ΔV =

Current in each resistor?

Total resistance = 6 Ω

Ohm’s Law: I = V / R = 12 V / 6 Ω

= 2 A

Voltage drop across resistor?

V = I R

12 V I

PHYS 1022: Chap. 31-32, Pg 36

–I2R1 –I2R2

+ε

Start + ε – I2R1 – I2R2 ΔV = = 0

+ I3R3

–ε

Start – ε + I3 R3 ΔV = = 0

The first thing we have to do is? Define currents!

I1

I2

I3

Now apply Loop rule to each loop R1 R2

R3

Next: Define travel direction: top loop (CW)

bottom loop (CW)

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