circuit with resistor and inductor

[logistic_guy]

Determine \(\displaystyle \bold{I}_s\) in the circuit shown if the voltage source supplies \(\displaystyle 2.5 \ \text{kW}\) and \(\displaystyle 0.4 \ \text{kVAR}\) (leading).

 

[khansaheb]

Determine \(\displaystyle \bold{I}_s\) in the circuit shown if the voltage source supplies \(\displaystyle 2.5 \ \text{kW}\) and \(\displaystyle 0.4 \ \text{kVAR}\) (leading).

View attachment 39054

show us your effort/s to solve this problem.

 

[barbsabbs]

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[logistic_guy]

For now it's obvious that both currents: the current coming from the current source and the current coming from the voltage source, are entering the the resistor and the inductor.

Let \(\displaystyle \bold{I}_v\) be the current of the voltage source.

And

Let \(\displaystyle \bold{I}_z\) be the current in the resistor and inductor.

Then

\(\displaystyle \bold{I}_z = \bold{I}_s + \bold{I}_v\)

We have three unknowns and we have to figure out a way to find two of them!

Thinking....

 

[logistic_guy]

If you solved simple \(\displaystyle \text{DC}\) circuits, I am sure that you would be familiar with ohm's law:

\(\displaystyle V = I \times R\)

Now even if we have \(\displaystyle \text{AC}\) circuits and combinations of resistors, inductors, and capacitors, the law stays the same, but instead of \(\displaystyle R\), we write \(\displaystyle \bold{Z}\).

where \(\displaystyle \bold{Z}\) is called impedance. The impedance is just the combination of \(\displaystyle R\) and \(\displaystyle L\) (inductor) in our current circuit.

So, we have this formula:

\(\displaystyle \bold{V} = \bold{I}_z \times \bold{Z}\)

This formula will help us solve for \(\displaystyle \bold{I}_z\).

\(\displaystyle \bold{I}_z = \frac{\bold{V}}{\bold{Z}} = \frac{120}{8 + j12} \ \text{A}\)

In the next post, we will try to figure out a way to find the current, \(\displaystyle \bold{I}_v\).