[Electrical Engineering]Finding current with mesh analysis(ac)

[equalP]

Homework Statement

The question asks me to find i_o by using mesh analysis.

Homework Equations

KCL

The Attempt at a Solution

In fact, the question also asks me to find it by superposition and I found the answer should be:
i₀=0.1+0.218 cos⁡(2000t+134°)-1.18 sin⁡(4000t+7.4°)

But I don't know how to use mesh analysis to solve the circuit with independent sources of different frequency.

Thanks for reading my post.

 

[gneill]

Homework Statement

The question asks me to find i_o by using mesh analysis.

Homework Equations

KCL

The Attempt at a Solution

In fact, the question also asks me to find it by superposition and I found the answer should be:
i₀=0.1+0.218 cos⁡(2000t+134°)-1.18 sin⁡(4000t+7.4°)

But I don't know how to use mesh analysis to solve the circuit with independent sources of different frequency.

Thanks for reading my post.

Hi equalP; Welcome to Physics Forums.

The idea behind using superposition is that you can solve for the effect of each source independently (by suppressing the others), then sum the results.

 

[equalP]

Hi equalP; Welcome to Physics Forums.

The idea behind using superposition is that you can solve for the effect of each source independently (by suppressing the others), then sum the results.

Is it possible for me to solve this problem by using mesh analysis directly?

 

[gneill]

Is it possible for me to solve this problem by using mesh analysis directly?

No, the impedances of the reactive elements are different for different frequencies. As a result, each source "sees" a different network, which will make the impedance matrices differ.

 

[equalP]

No, the impedances of the reactive elements are different for different frequencies. As a result, each source "sees" a different network, which will make the impedance matrices differ.

Thank you. And I think the assignment may want me to write down it is impossible and explain why.