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

Question

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 (A) 1,5,6 (B) 1.5,2.5,8 (C) 2,3,7 (D) 2,4,6

Tardigrade Admin · Accepted Answer

C1 + C2 + C3 = 12 , C1C2 C3 = 48 and C1 + C2 = 6 i.e. 6 + C3 = 12 i.e. C3 = 6 unit Using C1 C2 C3 = 48 , we get C1 C2 = (48/6) = 8 Solving C1 = 2 unit and C2 = 4 unit

Q. The equivalent capacitance of three capacitors of capacitance C1​,C2​andC3​ 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

1,5,6

1.5,2.5,8

2,3,7

2,4,6

C1​+C2​+C3​ = 12 , C1​C2​C3​ = 48 and C1​+C2​ = 6 i.e. 6 + C3​ = 12 i.e.C3​ = 6 unit Using C1​C2​C3​ = 48 , we get C1​C2​=648​=8 Solving C1​ = 2 unit and C2​ = 4 unit

$C_{1} + C_{2} + C_{3}$ = 12 , $C_{1} C_{2} C_{3}$ = 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