If-R-1-j-L-R-3-R-2-R-4-j-1-C-where-R-1-R-2-R-3-R-4-L-and-C-are-real-show-that-L-C-R-2-R-3-2-C-2-R-4-2-1-

Question Number 51248 by Tawa1 last updated on 25/Dec/18

If \frac{R_{1} + j ω L}{R_{3}} = \frac{R_{2}}{R_{4} - j \frac{1}{ω C}}, where R_{1}, R_{2}, R_{3}, R_{4}, ω, L and C

are real, show that L = \frac{C R_{2} R_{3}}{ω^{2} C^{2} R_{4}^{2} + 1}

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

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

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

L = \frac{R_{3}}{w} \times \frac{\frac{R_{2}}{w C}}{\frac{R_{4} w^{2} C^{2} + 1}{w^{2} C^{2}}}

L = \frac{R_{3}}{w} \times \frac{R_{2} w^{2} C^{2}}{w C (R_{4} w^{2} C^{2} + 1)} = \frac{R_{2} R_{3} C}{1 + R_{4} w^{2} C^{2}}

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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