If ((R_1 + jωL)/R_3 ) = (R_2 /(R_4 − j (1/(ωC)))) , where R_1 , R_2 , R_3 , R_4 , ω, L and C are real , show that L = ((C R_2 R_3 )/(ω^2 C^2 R


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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

	$t h a n k y o u . . .$
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