Theory And Calculations

Copyright 1999-2015 Dan Dudley

Ohm’s Law and Voltage Drop

Ohm’s Law

Theory

And

Calculations

8/29/2016 Copyright 2016 Dan Dudley & Associates



Code Basics

• 110.5 Cu conductors unless otherwisestated.

• 110.14(c) Temp. not to exceed lowestconnected device or component.

• High Voltage – > (over) 600 Volts• 220.2(b) can drop fraction less than .5• Appendix-D Major fraction (.5 or higher)




Ohm’s Law Wheel

Value youare lookingto solve




Ohm’s Law Wheel

Values that youare given in thequestion




W

Perform theSquared

Value first

Multiplythen

performthe Ö




Ohm’s Law Theory

• There is a direct relationship betweenVoltage, Current, and Resistance.

• The Rate of flow of the current is equal tothe Electromotive Force divided by theResistance.




Voltage and Current

• Voltage and Current are directlyproportional– Increase one – Increase the other– Decrease one – Decrease the other

• Current and Resistance are inverselyproportional– Increase Resistance – decrease Current– Decrease Resistance – Increase Current




Ohm’s Law basics:• Voltage and Current are directly proportional

– When the Voltage is increased the current increasesproportionately.

– When the Voltage is decreased the current decreasesproportionately.

• I = Intensity of Current in Amperes• E = Electromotive Force in Volts• R = Resistance in Ohms• P = Power in Watts or Volt Amps




Example #1Voltage Current Relationship

• The Voltage in the circuit is 120V, theresistance is 200 ohms, and the current is.6 amps.

– If the voltage is increased to 240 Volts, theamperage will increase to amps.

– Use I = E / R to prove this.1.2





• The Voltage in the circuit is 120 V, theresistance is 50 ohms, the current is 2.4amps.

– If the voltage is decreased to 12 volts, theamperage (current) will decrease to .24 amps.

– The voltage is 1/10 original value and theAmperage is now 1/10 the original value.





• The Voltage in the circuit is 120V, theresistance is 5 ohms, the current is 24amps.

– If the resistance is increased to 7 ohms, theamperage (current) will decrease to 17 amps.

– Resistance is opposition to current flow.




Resistance Formulas

• Series:

–RT = R1 + R2 + R3 …




Parallel Resistance Formulas

• Parallel:

– RT =

– RT =

R1 X R2R1 + R2

R of one# of R’s

2 unequal sizeResistances in

parallel

2 or more equalsize resistances

In parallel




• Unequal parallel – any number

1

1/R1 + 1/R2 + 1/R3

Divide all parallel resistances into “1”, add them allTogether and divide that number into “1” this is the

Actual resistance

More than 2 unequal parallel resistances




RT = 11/R1 + 1/R2 + 1/R3

11/2 + 1/3 + 1/7

RT =

1.5 + .333 + .1428

RT =

1.9758

RT =

RT = 1.024 ohms




Calculator Format

1 ¸ 2 = M+

1 ¸ 3 = M+

1 ¸ 7 = M+

1 ¸ MRC =

.5

.333

.1428

1.02439 ohms




What is RT and IT forthis Circuit ?

Source120Volts

R1 = 4ohms

R2 = 8ohms

Resistance in Series –Add Together

RT = R1 + R2 = 12 ohms

Current in Series Circuit

IT = E / R = 120 / 12

= 10 amps

Current in = Current out




E = R X I E = W / I E = ÖW X R

R = 12 ohms

Load

1200

Watts

What is the voltage of this circuit ?

E = ÖW X R = Ö1200 W X 12 ohms = 120 V




R = E / I R = E2 / P R = W / I2

What is the resistance of this circuit ?

R = E2 / W = (120 V X 120 V) / 1200 Watts

= 14,400 V / 1200 Watts

= 12 Ohms

120 V source

Load

1200 W




R = E / I R = E2 / P R = W / I2

What is the resistance of this circuit ?

R = W / I2 = 1200 W / (10 A X 10A)

= 1200 W / 100 Amps

= 12 Ohms

Load

1200 WI = 10 Amps




I = E / R I = W / E I = ÖW / R

R = 12 ohms

What is the current of this circuit ?

I = ÖW / R = Ö1200 W / 12 ohms = 10 A

1200 W




W = E X I W = R X I2 W = E2 / R

R = 12 Ohms

What is the wattage of this circuit ?

W = E2 / R = (120 V X 120 V) / 12 Ohms

= 14,400 / 12 Ohms

= 1200 W

120 V




120 V

S5ê

R6 = 8 WR5 = 2 W

R4 = 4 W

R7 = 4 W

R8 = 4 W

S7ê

R9 = 10 W

R3 = 8 W

R2 = 6 W

R1 = 2 W

S6êS2ê

S1ê

S3ê

S4




120 V

S5ê

R6 = 8 WR5 = 2 W

R4 = 4 W

R7 = 4 W

R8 = 4 W

S7ê

R9 = 10 W

R3 = 8 W

R2 = 6 W

R1 = 2 W

S6êS2ê

S1ê

S3ê

S4

18 Ohms




120 V

S5ê

R6 = 8 WR5 = 2 W

R4 = 4 W

R7 = 4 W

R8 = 4 W

S7ê

R9 = 10 W

R3 = 8 W

R2 = 6 W

R1 = 2 W

S6êS2ê

S1ê

S3ê

S4

6.428 Ohms8/29/2016 Copyright 2016 Dan Dudley & Associates



In a ‘Purely’ RESISTIVE circuit theVOLTAGE and CURRENT are in PHASE

Voltage MAX

Current MAX

¼ Cycle

1/2 Cycle

1 Cycle




ELI the ICE manIn a Purely Resistive circuit: Voltage and Currentare in Phase. The phase angle is (0) zero.

Both Voltage and Current are at Max and Min atthe same time.




ELI the ICE manIn a Purely Inductive circuit: Voltage leads Currentby 90 degrees or Current lags Voltage by 90degrees




ELI the ICE manIn a Purely Capacitive circuit: Current leadsVoltage by 90 degrees or Voltage lags Current by90 degrees




Peak = 100%

Eff = 70.7%

Avg = 63.7%

Peak

Peak Effective

Avg

Effective

Avg

What does your volt meter read? Effective


Theory And Calculations

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