Chromalox Big Red Book

Technical

Technical Information Electrical Fundamentals & Three Phase Calculations

OHM’S LAW

Voltage & Wattage Relationships An electric resistance element only produces rated Wattage at rated Voltage. It is common for electric heating elements and assemblies to be connected to a wide range of operating Voltages. Since the Wattage output varies directly with the ratio of the square of the Voltages, the actual Wattage can be calculated for any applied Voltage. The relationship is expressed by the equation below, Where: W a = Actual Wattage 2 W r = Rated Wattage W a = W r x V a V a = Applied Voltage V r V r = Rated Voltage ( ) Ohm’s Law The relationship between Wattage (heat) output and the applied Voltage of electric resistance heating elements is determined by a precise physical rule defined as Ohm’s Law which states that the current in a resistance heating element is directly proportional to the applied Voltage. Ohm’s Law is traditionally expressed as: Where: I = Amperes (Current) I = E E = Voltage R R = Ohms (Resistance) The same equation using the conventional ab- breviation for voltage is: Where: I = Amperes (Current) I = V V = Voltage R R = Ohms (Resistance) An unknown electrical value can be derived by using any two known values in one of the varia- tions of Ohm’s Law shown at the right. Three Phase Equations (Balanced) Ohm’s Law, as stated above, applies to electri- cal resistance elements operated on single phase circuits. Ohm’s Law can be modifed to calculate three phase values by adding a correction factor for the phase Voltage rela- tionships. The three phase equations shown can be applied to any balanced Delta or Wye circuit. The terms used in the equations are identified below: 2 I l = Line Current (Amps) I p = Phase Current (Amps) W t = Total Watts R 1 = R 2 = R 3 = Element Resistance Wc = Wattage per Circuit (Equal Circuits) Rc = Circuit Resistance in Ohms Measured Phase to Phase V l = Line Voltage V p = Phase Voltage

VOLTS

AMPERES

VOLTS = WATTS X OHMS

AMPERES= VOLTS OHMS

WR V

R W V

W I

VOLTS = WATTS AMPERES

AMPERES= WATTS VOLTS

W R

VOLTS = AMPERES X OHMS

AMPERES= WATTS OHMS

V (VOLTS) (OHMS) R

I (AMPS) (WATTS) W

V I IR

OHMS

WATTS

VI

OHMS = VOLTS AMPERES

WATTS = VOLTS x AMPERES

I 2 R

W I 2

V 2 R

V 2 W

OHMS = WATTS AMPERES 2

WATTS = AMPERES 2 x OHMS

OHMS = VOLTS 2 WATTS

WATTS = VOLTS 2 OHMS

Percent of Rated Wattage for Various Applied Voltages

Rated Voltage 110 115 120 208 220 230 240 277 380 415 440 460 480 575

Applied Voltage

110 115 120 208 220 230 240 277 380 415 440 460 480 550 575 600

100 109 119

91 100 109

84 92 100 300

28 31 33

25 27 30 89

23 25 27 82 91 100 109 — — —

21 23 25 75 84 92 — — — — — — — —

16 17 19 56 63 69

8.4 9.0 10 30 34 37 40 53 100 119

7.0 7.6 8.4 25 28 31 33 45 84 100 112 123

6.2 6.7 7.4 22 25 27 30 40 74 89 100 109 119 156 171 186

5.7 6.2 6.8 20 23 25 27 36 68 81 91 100 109 143 156 170

5.2 5.7 6.3 19 21 23 25 33 63 75 84 92 100 131 144 156

3.7 4.0 4.3 13 15 16 17 23 44 52 58 64 70 91 100 109

— — — — — — — — — — — — —

— — — — — — — — — — — — —

100 112 122 133 — — —

— — — — — — — — — — — —

100 109 119 — — —

100 133

75 100 188 —

— — — — — —

— — — — — —

— — — — — —

— — — — — —

— — — — — —

— — — —

3Ø Wye

3Ø Delta

I

L

I

V

P

P

R

R

R

V

1

2

2

P

V

L

I

V

P

L

R

1

R

R

3

3

I

I

L

L

V p = V l

V l = V p

V p = V l ÷ 1.73 W t = 1.73 I l x V l

V l = V p x 1.73 W t = V l 2 ÷ R 1

W t = 1.73 I l x V l I p = I l ÷ 1.73

W t = 3 (V l 2 ÷ R 1 ) I l = I p x 1.73

I p = I l

I l = I p

W c = 1.73 I l x V l ÷ # Circuits R c = (2 x V l 2 ) ÷ W c R c = V l 2 ÷ 0.5W c Note — For Open Delta connections, see next page.

W c = 1.73 I l x V l ÷ # Circuits R c = (2 x V l 2 ) ÷ W c R c = V l 2 ÷ 0.5 W c Note — For Open Wye connections, see next page.

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