Explain clearly the method of representing a vector quantity by the notation?

Question

A circuit consists of a resistance of 20 ohms in series with an inductance of 0.6 henry. The frequency is 79.5hz. If the potential differences across the circuit is represented by 40 + j25 volts, find (a) the complex expression for the current, (b) the magnitude of the current, (c) the phase angle

Answer 1

You're familiar with the standard cartesian coordinate system in two dimensions. You know, the basic X-Y graph? Well, just plot the real component on the x axis, and the imaginary component on the y axis. So, you go over 40 on the x axis, and up 25 on the y axis (imaginary axis now). Plot the point (40,25). Draw a line from the origin to the point you just plotted. There you go. You've plotted the voltage vector for the circuit.

In the voltage expression, the 40 was the real component, and the 25 was the imaginary component. To find the magnitude, do some simple geometry. You know the lengths of the sides, now find the length of the hypotenuse. Hint: sqrt(40^2 + 25^2).
The phase angle is the angle of the vector from the x axis, going counterclockwise. So just take tan^(-1) of 25/40 to find the angle of the voltage vector. Now that you know how to find the magnitude and phase angle of a complex number, you can apply the same principles to find the answer to the problem.

Now, i = v/Z.
v = (40+j25)
Z = add resistor plus inductor: 20 ohms + j*2pi*freq*L
So you divide this to find the current: (40 + j25)/(20+ j*79.5*2*pi*0.6)
You can do this by plugging in numbers on a calculator that handles imaginary numbers. The answer will be the complex expression of the current. It will have a real and an imaginary component. Use what I taught you to find the magnitude and the phase angle.