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show that Rs = R3R1/R2, in a balanced bridge : R3 * ( R1+ L1 ) = R2 (Ls+Rs), using the fact that quality factors wLs/Rs = wL1/R1

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Solution

Sure, let's solve this step by step:

  1. Given the quality factors ωLs/Rs = ωL1/R1, we can rearrange this equation to Rs = ωLs/ωL1 * R1. This is equation [1].

  2. We are also given that in a balanced bridge, R3 * (R1 + L1) = R2 * (Ls + Rs). We can rearrange this equation to Rs = R3 * R1/R2 - L1. This is equation [2].

  3. Now, we can equate the two expressions for Rs from equation [1] and equation [2]. This gives us ωLs/ωL1 * R1 = R3 * R1/R2 - L1.

  4. Simplifying this equation, we get Rs = R3 * R1/R2.

So, we have shown that Rs = R3R1/R2 in a balanced bridge using the given conditions.

This problem has been solved

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