- #1

MFletch

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The answer needs to be in rectangular and polar form.

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- MHB
- Thread starter MFletch
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In summary, the person is asking for help with a math problem. They need to find the admittance of a Z-wave module, and they are having trouble with the simplified rectangular form. They also mention that the values might be impedances or admittances, but they are not sure.

- #1

MFletch

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The answer needs to be in rectangular and polar form.

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- #2

DavidCampen

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- #3

MFletch

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Thank you, however, How would that convert to polar and Rec. form?

- #4

DavidCampen

- 65

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$$\frac{55{(j-1)}^{2}}{16(j-1)} = ?$$

Hint, cancel like terms and you will have the rectangular form.

so the rectangular form will be

$$\frac{55}{16}(j-1)$$

Hint, cancel like terms and you will have the rectangular form.

so the rectangular form will be

$$\frac{55}{16}(j-1)$$

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- #5

MFletch

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What would be the best way to find the admittance of Z = (1/5j-1) + (1/2j+6) + (1/4j) in rectangular and polar form?

- #6

DavidCampen

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MFletch said:

What would be the best way to find the admittance of Z = (1/5j-1) + (1/2j+6) + (1/4j) in rectangular and polar form?

Add the imaginary parts together and separately add the real parts together to get the simplified rectangular form (aj + b) then you can convert to polar form by finding the magnitude = $\sqrt{{a}^{2}+{b}^{2}}$ and the angle = ${tan}^{-1}(\frac{a}{b})$

- #7

MFletch

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I’m not sure I follow

- #8

DavidCampen

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"What would be the best way to find the admittance of Z = (1/5j-1) + (1/2j+6) + (1/4j) in rectangular and polar form?"

Add together the 3 three terms given above. The first two terms are$ (\frac{1}{5}j-1)$ and $ (\frac{1}{2}j+6)$, what is the sum?

Hint:

What is the sum of $ \frac{1}{5}j$ and $ \frac{1}{2}j$?

What is the sum of -1 and 6?

I see also that this question is asking for admittance which is the reciprocal of impedance. So proceed as above to find the impedance in rectangular form and then find the reciprocal of that.

Add together the 3 three terms given above. The first two terms are$ (\frac{1}{5}j-1)$ and $ (\frac{1}{2}j+6)$, what is the sum?

Hint:

What is the sum of $ \frac{1}{5}j$ and $ \frac{1}{2}j$?

What is the sum of -1 and 6?

I see also that this question is asking for admittance which is the reciprocal of impedance. So proceed as above to find the impedance in rectangular form and then find the reciprocal of that.

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- #9

skeeter

- 1,103

- 1

MFletch said:What would be the best way to find the admittance of Z = (1/5j-1) + (1/2j+6) + (1/4j) in rectangular and polar form?

just checking. do you mean ...

$Z = \left(\dfrac{1}{5} j - 1 \right) + \left(\dfrac{1}{2} j + 6 \right) + \left(\dfrac{1}{4} j \right)$

or ...

$Z = \dfrac{1}{5j - 1} + \dfrac{1}{2j + 6} + \dfrac{1}{4j}$

- #10

MFletch

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skeeter said:just checking. do you mean ...

$Z = \left(\dfrac{1}{5} j - 1 \right) + \left(\dfrac{1}{2} j + 6 \right) + \left(\dfrac{1}{4} j \right)$

or ...

$Z = \dfrac{1}{5j - 1} + \dfrac{1}{2j + 6} + \dfrac{1}{4j}$

the second equation

- #11

skeeter

- 1,103

- 1

skeeter said:just checking. do you mean ...

$Z = \left(\dfrac{1}{5} j - 1 \right) + \left(\dfrac{1}{2} j + 6 \right) + \left(\dfrac{1}{4} j \right)$

or ...

$Z = \dfrac{1}{5j - 1} + \dfrac{1}{2j + 6} + \dfrac{1}{4j}$

MFletch said:the second equation

That's what I thought. In future, use grouping symbols to set off the denominators like so ...

$Z = \dfrac{(2j+6)(4j)}{(5j - 1)(2j+6)(4j)} + \dfrac{(5j-1)(4j)}{(5j-1)(2j + 6)(4j)} + \dfrac{(5j-1)(2j+6)}{(5j-1)(2j + 6)(4j)}$

$Z = \dfrac{(24j-8)-(4j+20)+(28j-16)}{(5j-1)(2j + 6)(4j)}$

$Z = -\dfrac{48j - 44}{64j+112}$

can you complete the simplification from here?

- #12

DavidCampen

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Then, instead of writing "Z = (1/5j-1) + (1/2j+6) + (1/4j)" you should have written something like "Z = 1/(5j-1) + 1/(2j+6) + 1/(4j)" .MFletch said:the second equation

Also, are the values impedances or admittances? This can't be determined just by looking at the complex numbers though the "Z = " could be construed to imply that they are impedances.

Also, why do you write the imaginary part of the complex number before the real part? Usually it is written the other way around.

Impedance is a measure of the opposition that a circuit presents to the flow of alternating current (AC). It is represented by the symbol Z and is measured in ohms (Ω).

In rectangular form, impedance is calculated using the formula Z = R + jX, where R is the resistance in ohms and X is the reactance in ohms. This formula takes into account both the resistance and reactance components of impedance.

In polar form, impedance is calculated using the formula Z = |Z|∠θ, where |Z| is the magnitude of impedance and ∠θ is the phase angle in degrees. This formula represents impedance as a vector with magnitude and direction.

The rectangular form of impedance takes into account both the resistance and reactance components, while the polar form represents impedance as a magnitude and phase angle. Both forms can be converted to each other using mathematical equations.

Knowing the impedance of a circuit is important because it helps in understanding the behavior of the circuit when an AC current is applied. It also helps in calculating the power, voltage, and current in the circuit, which is crucial in designing and analyzing electrical systems.

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