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1) Here is the capacitor matrix:
Q1=b12*V1 + b12*V2 + b13*V3
Q2=b21*V1 + b22*V2 + b23*V3
Q3=b31*V1 + b22*V2 + b33*V3
How would you express the bij coefficients in terms of
what is given? [geometry, etc.]
Suppose the values of these coefficients are given.
How to express C12 in terms of these coefficients?
By C12 I mean the capacitance a battery would see
if it were connected to leads attached to vertical plates?
3) JohnD provided a hint "V = C^-1 Q, for imposed Q"