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25 Overview

• electric current & circuits

• Ohm’s Law

• energy

• Kirchoff’s Rules

• RC circuits

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Current: Charge Flow• I = Q/t (coulomb/second = ampere, A)

• affected by material and field

• carriers: electrons or “holes”

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dqnAvI

current parameters

• q = charge/carrier

• n = carriers/volume

• A = cross-section

• vd = drift velocity

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Conductors• F = qE moves charges

• V = -EL

• Vb < Va

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Electrical Resistance

I

VR ohm, [volt/amp]

Example: 6.0V causes 0.1A current:

601.0

0.6

A

V

I

VR

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Ohm’s Law• many materials have constant V/I

• e.g. 2V causes 2I (2V/2I = V/I)

• called “Ohmic”

OhmicNon-Ohmic

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Example Non-Ohmic: Diode

Sizeable current flows in only one direction

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Example Diode Application

Half-Wave Rectifier

Full-Wave Rectifier

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Resistivity“specific resistance”

• Intrinsic (does not depend on shape)

• Resistance is Extrinsic (depends on shape)

• Symbol: (“rho”).

• SI Unit: ohm-meter (-m)

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Factors Affecting Resistivity

• Temperature

• Defects

• Impurities

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some resistivities @ 20C

• nm m

• silver 16

• copper 17

• aluminum 28

• nichrome 1000

• silicon 640

• insulators 108 to 1016

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Resistance & Resistivity

A

LR where is the “Shape-Factor”

A

L

Example: R = 3ohms, L = 15m, A = 10-6 m2

mnm

m

L

RA

20015

)10)(3( 26

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Energy Dissipated in a Resistor

VQU

Vt

Q

t

U

PPowert

U,

ICurrentt

Q,

VIP

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Circuit Analogy

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“Terminal Voltage” Real Battery

internal battery resistance

load resistor

IrV

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Combinations of Resistors

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Connection Types

Series

Parallel

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Equivalent Resistances

21 RRReq

112

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RRReq

Series

Parallel

Ex. R1 = 4, R2 = 12: Req = 4 + 12 = 16 ohms

Ex. R1 = 4, R2 = 12: Req = (4-1 + 12-1)-1 = 3 ohms

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Ex. Calc: equivalent resistance, current, voltages, powers dissipated

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Ex. Calc: equivalent resistance, current, voltages, powers dissipated

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Calc: equivalent resistance

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Kirchhoff’s Rules

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Kirchoff’s Rules:1. Loop Rule.

2. Junction Rule.

outin II

0 V

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I1 I2II = I1 + I2 (junction)

0)( 111321 RIRII

ab

a

b 022211 RIRI

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0)( 111321 RIRII 022211 RIRI

V0.11 V0.22 0.11R 0.22R 0.33R

013)( 121 III

022 21 II

0134 21 II

)022(4 21 II 0134 21 II

07110 2 I

0134 21 II11/72 I

12 413 II 11

72

I

)1)(3( 117

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1 I

))(( 1111

1121

41

1 I

4432

1 I

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Calc: I = 2A, I2 = 0.5A, I1 = 1.5A

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Ammeter: small r (Req = R)

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Voltmeter: large r (Req = R)

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RC Circuits

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Charging/Discharging C’s

• Resistance affects time required

• Capacitance value also affects time needed

• time constant = RC.

• Benchmarks values related to e = 2.718

• discharge: 1/e = 0.3678, Q @ t = RC

• charge: 1 – 1/e = 0.6321, Q @ t = RC

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Summary

• electric current is + flow of charge/time

• V = IR R = L/A

• P = I2R

• circuits obey charge and energy cons.

• RC = exponential time constant

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