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  4. The equivalent capacitance of three capacitors of capacitance C1, C2 and C3 connected in parallel is 12 units and the product C1, C2 C3 = 48. When the capacitors C1 and C2 are connected in parallel the equivalent capacitance is 6 units. Then the capacitances are

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

KCETKCET 1999Electrostatic Potential and Capacitance

Solution:

$C_1 + C_2 + C_3 $ = 12 , $C_1C_2 C_3$ = 48 and $C_1 + C_2 $ = 6
$i.e.$ 6 + $C_3 $ = 12 $i.e. \, C_3 $ = 6 unit
Using $C_1 C_2 C_3 $ = 48 , we get $C_1 C_2 = \frac{48}{6} = 8 $
Solving $C_1 $ = 2 unit and $C_2$ = 4 unit