Finding voltage and impedance

[MissP.25_5]

Hi again. I just want to make sure I got the answers correct since this is a past year question (received from a senior), I don't have the answers.

Power supply voltage E=10e^(jπ/4) [V]; Current I1=2e^(jπ/4) [A].
The magnitude of current I2 is equals to current I1, but its phase is π/2 slower than I1.
1) Find the voltage V.
2)Find impedance Z.

 

[phinds]

Hi again. I just want to make sure I got the answers correct since this is a past year question (received from a senior), I don't have the answers.

Power supply voltage E=10e^(jπ/4) [V]; Current I1=2e^(jπ/4) [A].
The magnitude of current I2 is equals to current I1, but its phase is π/2 slower than I1.
1) Find the voltage V.
2)Find impedance Z.

Show your work.

 

[gneill]

Hi again. I just want to make sure I got the answers correct since this is a past year question (received from a senior), I don't have the answers.

Power supply voltage E=10e^(jπ/4) [V]; Current I1=2e^(jπ/4) [A].
The magnitude of current I2 is equals to current I1, but its phase is π/2 slower than I1.
1) Find the voltage V.
2)Find impedance Z.

Yep. Your work looks fine.

 

[MissP.25_5]

Yep. Your work looks fine.

Thanks!I am posting a couple more works that I've done. I hope you don't mind checking.

 

[rezeew]

Hello! It's great that you are double-checking your answers to previous questions. Let's work through these together to make sure you have the correct solutions.

1) To find the voltage V, we can use Ohm's Law which states that V = IR, where V is voltage, I is current, and R is resistance. In this case, we are given the current I1 and we can find the impedance Z from the second part of the question. So, V = I1 * Z. Using the given values, we get V = 2e^(jπ/4) * Z. We can also write this in polar form as V = 2∠π/4 * Z. To solve for Z, we can divide both sides by 2 and take the inverse of the complex exponential, giving us Z = V/2∠π/4. Plugging in the given voltage E, we get Z = (10e^(jπ/4))/2∠π/4. Simplifying this, we get Z = 5e^(jπ/4).

2) To find the impedance Z, we can use Ohm's Law again, but this time we have both the voltage E and current I2. So, Z = E/I2. Plugging in the given values, we get Z = (10e^(jπ/4))/(2e^(jπ/4) * e^(jπ/2)). Simplifying this, we get Z = (10e^(jπ/4))/(2e^(3π/4)). We can then use the properties of complex exponential to simplify this further, giving us Z = (5/√2)e^(jπ/4). This is the impedance in polar form. To convert it to rectangular form, we multiply the magnitude by cos(π/4) and sin(π/4) for the real and imaginary parts respectively. So, Z = (5/√2) * (cos(π/4) + jsin(π/4)). Simplifying this, we get Z = (5/√2)(√2/2 + j√2/2). Finally, we get Z = 5/2 + j5/2.

I hope this helps and let me know if you have any further questions. It's always good to double-check and make sure we have the correct solutions.