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
Question
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
Solution
Sure, let's solve this step by step:
-
Given the quality factors ωLs/Rs = ωL1/R1, we can rearrange this equation to Rs = ωLs/ωL1 * R1. This is equation [1].
-
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].
-
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.
-
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.
Similar Questions
The correct equation for this Wheatstone bridge isa.Rx= R3 (R2 / R1)b.None of thesec.Rx=V R3 (R1 / R2)d.Rx= R3 (R1 / R2)e.Rx=V R3 (R2 / R1)
series resonant circuit has R = 2 Ω, L = 1 mH and C = 0.1 μF, the value of quality factor Q is:
Wheatstone bridge with P=250Ω, Q=100Ω, R=1500Ω, S=600Ω. This Wheatstone bridge is_____________
Balance the unbalanced equation given and match each substance to the correct coefficient as indicated.Al2S3(s) + H2O(l) → Al(OH)3(aq) + H2S(g)
Balance the following chemical equation. (Remember to enter a "1" where you have a blank in front of a molecule/compound) AlBr3 + Cl2 --> AlCl3 + Br2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.