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Question Number 51250 by Tawa1 last updated on 25/Dec/18

Given that z_{1} = R_{1} + R + j ω L; z_{2} = R_{2}; z_{3} = \frac{1}{j ω C_{3}}

and z_{4} = R_{4} + \frac{1}{j ω C_{4}} and also that z_{1} z_{3} = z_{2} z_{4}, express

R and L in terms of the real constants R_{1}, R_{2}, R_{4}, C_{3} and C_{4}

Answer : R = \frac{R_{2} C_{3} - R_{1} C_{4}}{C_{4}}, L = R_{2} R_{4} C_{3}

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18

z_{1} z_{3} = z_{2} z_{4}

(R_{1} + R + j w L) \frac{1}{{j w C}_{3}} = R_{2} (R_{4} + \frac{1}{{j w C}_{4}})

c o m p a r i n g r e a l a n d i m a g i n a r y p a r t

\frac{R_{1} + R}{{j w C}_{3}} = \frac{R_{2}}{{j w C}_{4}}

R_{1} C_{4} + {R C}_{4} = R_{2} C_{3}

R = \frac{R_{2} C_{3} - R_{1} C_{4}}{C_{4}}

\frac{L}{C_{3}} = R_{2} R_{4} [L = C_{3} R_{2} R_{4}

Commented by Tawa1 last updated on 25/Dec/18

God bless you sir

Commented by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18

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