Equation Primers 1: Ohms Law / Power / Voltage Ratio.

Q1. How many watts of electrical power are used if 800V flows through a 800 Ω resistor?

Openoffice Math writeout:

P = {E^2} over {R}  
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p = {(800v) ^ 2} over {800 %OMEGA}
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p = 640000 over 800
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p = 800 w

Q2. How many watts of electrical power are used by a 12V dc light bulb that draws 100mA?

Openoffice Math writeout:

P = E x I
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P = 12v x 0.1A
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P = 1.2w (watts)

Q2. How many watts are dissipated when a current of 12A flows through a 4 ohm resistor? What is the applied voltage to produce this?

Openoffice math writeout:

P = (12A)^2 x 4 %OMEGA
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P = 144 x 4
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P = 576 w
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P = V^2 over R
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V = sqrt{P x R}
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V = sqrt{576w x 4 %OMEGA}
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V = sqrt{2304}
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V = 48v

Power Ratio / Voltage Ratio

Openoffice math writeout:

power ratio = log^-1(dB over 10)
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voltage ratio = log^-1(db over 20)

Q3. What is the power ratio of 12 dB?

Openoffice math writeout:

12dB = log^-1(12/10)
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log^-1(1.2)

Python equivalent function:

>>> 10**(12/10)
15.8489319

3db = doubling in power. 12 db = 3db doubled 4 times  or 2^4 (16)

Q4. What is the volatage ratio of 60db?

voltage ratio = log ^-1(dB over 20)

Openoffice math writeout:

60dB = log^-1(60 / 20)
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Ans: 1000

Python equivalent:

>>> 10**(60/20)
1000.0

Q5. Express a power ratio of 40% (10 log on power)

Openoffice math writeout:

10 log(40% / 100%)

Python equivalent:

>>>10 * math.log(0.4,10)
-3.979 db

Q6. Express a voltage ratio of 150% (20 log on voltage)

Openoffice math writeout:

20 log(150% / 100%)

Python Equivalent:

>>>20 * math.log(1.5,10)
3.52

Q7. 4dB represents a percentage voltage? (20 log on voltage)

Openoffice math writeout:

100% x log^-1(4/20)

Python equivalent:

>>>10**(4/20)
1.584893..