1. ## complex analysis

I have 2 questions.

Q1 In the following equation, by equating real and imaginary parts, find expressions for R6 and L in terms of R1, R2, R3, R4, R5 and C, given that the frequency is one radian per second.

R1-j/ωC = R2+R3
R4+R5 R6+jωL

Thanks

2. Originally Posted by Amy
I have 2 questions.

Q1 In the following equation, by equating real and imaginary parts, find expressions for R6 and L in terms of R1, R2, R3, R4, R5 and C, given that the frequency is one radian per second.

R1-j/ωC = R2+R3
R4+R5 R6+jωL

Thanks
Lets assume that $\displaystyle R_1, R_2, R_3, R_4, R_5, C \mbox{ and } L$ are all real and greater than zero, and that you mean:

$\displaystyle \frac{R_1-j/(\omega C)}{R_4+R_5}=\frac{R_2+R_3}{R_6+j \omega L}$

if $\displaystyle \omega=1$ this becomes:

$\displaystyle \frac{R_1-j/ C}{R_4+R_5}=\frac{R_2+R_3}{R_6+j L}$

Put $\displaystyle R_4+R_5=R_{4,5}$ and $\displaystyle R_2+R_3=R_{2,3}$, then we have:

$\displaystyle \frac{R_1-j/ C}{R_{4,5}}=\frac{R_{2,3}}{R_6+j L}$

and as none of the terms is zero flip this over to get:

$\displaystyle \frac{R_{4,5}}{R_1-j/ C}=\frac{R_6+j L}{R_{2,3}}$

On the left multiply top and bottom by $\displaystyle R_1+j/C$ and equate real and imaginary parts of both sides to get what you want.

RonL