Question

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 capacitance are :

• A. $1.5,2.5,8$
• B. $2,3,7$
• C. $4,2,6$
• D. $1,5,6$

Answer 1

The correct option is C $4,2,6$

$C_1,C_2$ and $C_3$ in parallel
$C_{eff}=C_1+C_2+C_3$
$12=C_1+C_2+C_3$ ------------ (1)
$C_1{C}_2{C}_3=48$ ------------ (2)
$C_1$ and $C_1$ are connected in parallel
$C_{eff}=C_1+C_2$
$C_1+C_2=6$--------(3)
from(1) and (3),
$C_3=6$
Hence equation (3) becomes
$C_1{C}_2=8$------(4)
also from (2)
$C_1=6-C_2$
$(6-C_2)C_2=8$
$C_2^2-6C_2+8=0$
solving this we get,
We get $C_1=4$, $C_2=2$, $C_3=6$