Circuits - AC circuits / phasor

[wcjy]

Homework Statement

Given the following circuit with the voltage source V=5 cos(t+θ) and the resistor R1=1.1(Ω) and the inductor L1=0.8(H). The impedance Z_eq of the circuit and the phasor current I can be respectively described as

$$Z_{eq} =a+jb $$
$$I= I_o ∠ Φ $$

Find a, b, and Io in these expressions.

Relevant Equations

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Hi, my school has no answer key provided. and would like to check if this is correct. Thanks!

 

[gneill]

Hi. It looks like you've correctly found the equivalent impedance and the magnitude of the current (both without units though). However, you'll need to account for the phase angle θ of the source in your I_o.

 

[wcjy]

Hi. It looks like you've correctly found the equivalent impedance and the magnitude of the current (both without units though). However, you'll need to account for the phase angle θ of the source in your I_o.

From the question, I_o is without phase angle. where I = I_o ∠ Φ. That is why i didn't account for the phase angle.

side note: how do you input latex for like I_o in the text

 

[Gordianus]

It's $I_{0}$ [sharp(#) sharp(#) I_{0} sharp(#) sharp(#) ]

 

[gneill]

From the question, I_o is without phase angle. where I = I_o ∠ Φ. That is why i didn't account for the phase angle.

Presumably you'll need to specify what $\Phi$ is, no?

 

[wcjy]

Presumably you'll need to specify what $\Phi$ is, no?

i don't need to but is it even possible, since they did not give angle $\theta$

 

[Gordianus]

You need $\theta$ to compute $\varphi$

 

[gneill]

i don't need to but is it even possible, since they did not give angle $\theta$

You can specify $\Phi$ in terms of $\theta$ and the impedance's angle.

 

[DaveE]

You can specify $\Phi$ in terms of $\theta$ and the impedance's angle.

Yes, phase shift matters in AC circuits.