R, lo Rx Rs Rx is the unknown resistance to be determined Rs is a variable stand
ID: 1874399 • Letter: R
Question
R, lo Rx Rs Rx is the unknown resistance to be determined Rs is a variable standard Ri and R2 are two (R,/R2) must be accurately known. G is a sensitive galvanometer and indicates resistance (usually accurate to within 0.1% or better). variable resistances the precise values of which are generally not needed but the ratio of which whether or not a current exists (charge flows) between C and D. The bridge is said to be "balanced" when the current through the galvanometer G is zero. It unknown, Rx can be expressed in terms of Rs, Ri, and R2. Working through the following questions should belp you to derive the equation relating Rx to the other resistances. When the bridge is balanced, IG When the bridge is balanced, 12-1 and Is When the bridge is balanced, Ve=V, I Therefore va-ve-v--V-, and Vc-VB-v--v-. Since R«V-V-, by substitution and asimilar equation we get R=RL Similarly, with an additional substitution before and another after, Ral-R_T If the last two equations are cormectiy obained you may divide one by the other, the current variables will cance leaving an equation in which Rx can be solved for: Since Rs and R,/R2 are, by assumption for this derivation and by design in real-world use, very accurately known, Rx= can be obtained very accurately.Explanation / Answer
In balanced condition:
(i) I(G) = 0
(ii) I(2) = I(1) & I(s) = I(x)
(iii) V(C) = V(D)
(iv) V(A) - V(C) = V(A) - V(D)
& V(C) - V(B) = V(D) - V(B)
(v) R(1)I(1) = V(A) - V(C)
& R(1)I(1) = R(x)I(x)
(vi) R(2)I(1) = R(s)I(s) = R(s)I(x)
(vii) R(x) = [R(1)R(s)]/R(2)
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