Solving Circuits Problem with 3 Equations

[Corneo]

Hi, I would like some hints on this problem here. I seem to have too many unknowns than equations that I can write. Assume that I am given the current for the three meshes and the two voltages. However I don't know anything about the components in the circuits.

I have these 3 equations, note that the currents I and V are all phasors. I just don't want to type \mathbf over and over again.

$$I_1 Z_4 + (I_1 - I_3)Z_{L_3} = V_{S_1}$$
$$(I_2- I_3)Z_{C_2} + I_2 Z_5 = V_{S_2}$$
$$I_3 R_3 + I_3 Z_{L_3} + (I_3 - I_2)Z_{C_2} + (I_3 - I_1)Z_{L_1} = 0$$

How can I solve for anyone of the components?

 

[OlderDan]

Hi, I would like some hints on this problem here. I seem to have too many unknowns than equations that I can write. Assume that I am given the current for the three meshes and the two voltages. However I don't know anything about the components in the circuits.

I have these 3 equations, note that the currents I and V are all phasors. I just don't want to type \mathbf over and over again.

$$I_1 Z_4 + (I_1 - I_3)Z_{L_3} = V_{S_1}$$
$$(I_2- I_3)Z_{C_2} + I_2 Z_5 = V_{S_2}$$
$$I_3 R_3 + I_3 Z_{L_3} + (I_3 - I_2)Z_{C_2} + (I_3 - I_1)Z_{L_1} = 0$$

How can I solve for anyone of the components?

If you have all the phasors, then you have more than three equations. Each of your equations can be divided into phase components (real and imaginary parts if you are using complex representation). Looks to me like you effectively have six equations and six unknowns.

 

[Corneo]

So your saying I should expand out the real and imaginary parts to get 3 more equations?

 

[OlderDan]

So your saying I should expand out the real and imaginary parts to get 3 more equations?

Yes. That's the way it looks to me. You can write the impedences as complex and you have the voltages and currents as complex. The reals must equal the reals and the imaginaries must equal the imaginaries.