Uab = Uam + Umb = (q1/c1) + (q1-q2)/q2 = q1/(c1+c2) -q5/c2 ; (1).
Uab = Uan + Unb = q3/c3 + (q5 + q3)/c4 = q3/(c3+c4) + q5/c4 ; (2).
Uab = Uab + Umn + Unb = q1/c1 + q5/c5 q3/c3 + q5/c4 = q1/c1 + q3/c4 + q5/(c5 + c4) ; (3).
(1) -> q1 = (Uab + q5/c2 )x( c1 + c2); (4).
(2)-> q3 = (Uab - q5/c4 )x( c3 + c4); (5).
(4)--->(3) = Uab = (Uab + q5/c2)x(c1 + c2 )xC1 + q5/(c5 + c4) + q3/c4
<=> Uabx( 1 - c1/(c1 + c2) = q5 :[ (c4 + c5 - c1c2/(c1 + c2)] + q3/c4. (6)
(5)--->(6) Uabx( 1 - c1/(c1 + c2) = q5 :[ (+ c5 - c1c2/(c1 + c2)] +
[Uab - (q5/c4)] / c4.
<=> Uab x [ c2/(c1 + c2) - c4/(c3 + c4)] = q5 :[ (+ c5 - c1c2/(c1 + c2) + c4xc4/(c3 + c4)]; ( 7).
ta có : C1xC4 = C2xC3 -> c2/(c1+c2) = c4/(c3 + c4) ;(
.
(
---->(7)--->q5=0--->Ucd=0 (dpcm)
