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The equivalent capacitance of three capacitors of capacitance $C_1, C_2$ and $C_3$ connected in parallel is $12$ units and their product is $C_1 \cdot C_2 \cdot C_3 = 48$. When the capacitors $C_1$ and $C_2$ are connected in parallel,the equivalent capacitance is $6$ units. Then the capacitances are:

Explain the necessity of the combination of capacitors and the ways of their connections.

Three long concentric conducting cylindrical shells have radii $R$,$2R$,and $2\sqrt{2}R$. The inner and outer shells are connected to each other. The capacitance across the middle and inner shells per unit length is:

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The equivalent capacitance between $A$ and $B$ in the given figure is

Find the equivalent capacitance between $A$ and $B$. (in $C$)

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