Question

_____R____________
| | |
|+ | XC
E1 XL |
|- | |+
| | E2
___________________-

Z1 = R= 4 ohms <0 4+-j0
Z2 = XL= 6 ohms <90. 0+j6
Z3 = XC=8 ohms <-90. 0-j8
E1= 10 v < 0. 10 +j0
E2= 40 v < 60. 20+j34.64

Please help me find the current up through R using mesh analysis.
I am having trouble because of the voltage polar angles.

My derivative is
(Z1+Z2) -Z2
-Z2 (Z2+Z3)
= Z1Z2 + Z1Z3 + Z2Z3

I1= E1. -Z2
-E2. Z2+Z3
=Z2(E1-E2) +Z3E1/D

I2=Z1+Z2. E1
-Z2. -E2
=-Z2(e1+e2)-Z1E2/D

Once the numbers and j's and polar angles get thrown around I have trouble keeping track. I'm not even sure if my I1 or I2 numerator is distributed correctly.

Answer 1

Okay well the circuit picture didn't figure very well. R is in series with e1 and XL
XL is in series on the other side with XC and e2

Answer 2

I = VR/R = 10/4 = 2.5A. = Current through all components(R,L, and C).

VL = I*XL = 2.5 * 6 = j15.0 Volts.

Vc = I*Xc = 2.5 * 8 = -j20.0 Volts.

Z = R + j(XL-Xc)) = 4 + j(6-8) =
4 - j2 = 4.47 Ohms[-26.6o].

Es = I*Z = 2.5 * 4.47 = 11.2 Volts.

Pf = Cos(-26.6) = 0.894 = Power factor.

P = I^2*R = 2.5^2 * 4 = 25 Watts.

Answer 3

Note: If the voltage across the resistor
is incorrect, all voltages will be wrong.