MATHEMATICS: Ratio, Proportion, Variation - Conductor wire Resistance, Reactance, Capacitance, Photograph exposure time, F stop of lens

RESISTANCE is inversely proportional to the SQUARE OF WIRE DIAMETER

example:

A wire AWG size 12 of 0.08 inches in diameter has a resistance of 15 ohms. Find the resistance of AWG 10 size conductor with a diameter of 0.10 in. Assume same length and same material.


given:

d1 = 0.08 in

R1 = 15 ohms

d2 = 0.10 in


find:

R2 = resistance of AWG 10 (diameter = 0.10 in)


solution:


R = k * 1/d^2

k = R * d^2

R1 * (d1)^2 = R2 * (d2)^2

15 * (0.08)^2 = R2 * (0.10)^2

R2 = 15 * (0.0064)/(0.10)^2

R2 = 15 * (0.0064)/(0.0100)

R2 = 9.6 ohms




CAPACITIVE REACTANCE is inversely proportional to CAPACITANCE

example:

If the capacitance of a circuit is increased by 50%, what percent will the capacitive reactance change?


given:

c1 = initial capacitance

c2 = 1.5 c1

R1 = initial capacitive reactance

R2 = final capacitive reactance


find:

%R = percent change in capacitive reactance corresponding to a 50% increase in capacitance


solution:


R = k/c

k = R * c

k = R1 * c1 = R2 * c2

R1 * c1 = R2 * c2

R1 * C1 = R2 * 1.5 C1

R1 = 1.5 R2  ---> equation 1


%R = [(R2 - R1)/R1] * 100%


substituting from equation 1,

%R = [(R2 - 1.5 R2)/1.5 R2] * 100%

%R = [-0.5/1.5] * 100%

%R = -33.33 % (negative value means decrease)

%R = 33.33 % decrease in capacitive reactance





TIME OF EXPOSURE is directly proportional to the SQUARE OF THE F STOP OF A LENS

example:

A photograph is exposed at a shutter speed of 0.02 seconds with a lens opening of f6. What shutter speed is required if lens opening is changed to f8.


given:

t1 = 0.02 sec

f1 = 6

f2 = 8


find:

t2 = shutter speed for a lens opening of f8



solution:


f stop of a lens = L/D


where:

L = focal length

D = diameter



t = k * f^2

k = t/f^2

t1/(f1)^2 = t2/(f2)^2

(0.02)/(6)^2 = t2/(8)^2

t2 = (0.02) * (8)^2/(6)^2

t2 = 0.02 * 64/36

t2 = 0.036 seconds