## How to Calculate and Solve for Phase Lag | Electromagnetic Method

The image above represents phase lag.

To compute for phase lag, three essential parameters are needed and these parameters are Frequency (f), Inductance (L) and Resistance (R).

The formula for calculating the phase lag:

φ = tan-1 (2πfL/R)

Where:

φ = Phase Lag
f = Frequency
L = Inductance
R = Resistance

Let’s solve an example;
Find the phase lag when the frequency is 20, the inductance is 32 and the resistance is 18.

This implies that;

f = Frequency = 20
L = Inductance = 32
R = Resistance = 18

φ = tan-1 (2πfL/R)
φ = tan-1 (2π(20)(32) / 18)
φ = tan-1 (4021.23 / 18)
φ = tan-1 (223.40)
φ = 89.74°

Therefore, the phase lag is 89.74°.

## How to Calculate and Solve for Depth of Penetration | Electromagnetic Method

The image above represents depth of penetration.

To compute for depth of penetration, two essential parameters are needed and these parameters are Conductivity (σ) and frequency (f).

The formula for calculating for depth of penetration:

d = 503.8 / √(σf)

Where:

d = Depth of Penetration
σ = Conductivity
f = Frequency

Let’s solve an example;
Find the depth of penetration when the conductivity is 12 and the frequency is 24.

This implies that;

σ = Conductivity = 12
f = Frequency = 24

d = 503.8 / √(σf)
d = 503.8 / √(12(24))
d = 503.8 / √(288)
d = 503.8 / 16.97
d = 29.68

Therefore, the depth of penetration is 29.68.

Calculating the Conductivity when the Depth of Penetration and the Frequency is Given.

σ = (503.8 / d)2 / f

Where;

σ = Conductivity
d = Depth of Penetration
f = Frequency

Let’s solve an example;
Find the conductivity when the depth of penetration is 20 and the frequency is 15.

This implies that;

d = Depth of Penetration = 20
f = Frequency = 15

σ = (503.8 / d)2 / f
σ = (503.8 / 20)2 / 15
σ = (25.19)2 / 15
σ = 634.53 / 15
σ = 42.30

Therefore, the conductivity is 42.30.

## How to Calculate and Solve for Angular Velocity | Motion

The image above represents angular velocity.

To Compute for angular velocity, one essential parameter is needed and the parameter is frequency (f).

The formula for calculating angular velocity:

ω = 2πf

Where;

ω = Angular Velocity
f = Frequency

Let’s solve an example;
Find the angular velocity when the frequency is 18.

This implies that;

f = frequency = 18

ω = 2πf
ω = 2 x π x 18
ω = 113.09

Therefore, the angular velocity is 113.09 rad/s.

## How to Solve and Calculate the Mean or Average of Discrete and Continuous Numbers

Mean is a measure of central tendency and is considered to be a very important parameter of statistics. Mean or Average is the sum of the data sets or numbers or values divided by the number of numbers or data sets or values.

What is a discrete number?

A discrete number is a standalone number. It might be a whole number or fractional number but it stands on its own with no extension or range. An example of a discrete number is 5, 12, 10.6, 17, 20

What is a continuous number?

A continuous number is a range of numbers packaged as a single entity. An example of a continuous number is 5 – 10, 20 – 30, 25 – 50.

There are two possibilities in calculating the mean of a set of discrete numbers. One can either compute the mean via the application of frequency or no frequency at all.

For Example: A set of discrete numbers such as these:

4, 5, 6, 7, 8, 9

These numbers all occur once and have a frequency of 1 per number.

Therefore, if you want to create a table for the number and frequency, it looks like this:

Number        4, 5, 6, 7, 8, 9

Frequency    1, 1, 1, 1, 1, 1

You can clearly see that there is no need for applying frequency to calculate the mean of the above set of numbers. Application of frequency on a large set of numbers makes it easier to organize and compute the mean.

Now, for a set of numbers such as these:

4, 4, 4, 2, 4, 5, 3, 3, 3, 2, 1, 1, 6, 4, 3, 2, 4, 2, 5, 2, 1

You can see that some of the discrete numbers occur more than once and this implies that application of frequency is useful and makes the computing of mean easier and comprehensive.

From the display of numbers above you can see that the number 4 occurred times, the number 2 occurred times, the number 5 occurred 2 times, the number 3 occurred 4 times, the number 1 occurred 3 times, the number 6 occurred 1 time.