Three capacitors of capacitances 2 μ F , 5 μ F , 8 μ F are connected first in parallel combination and then in series combination, The ratio of their equivalent capacitances will be

Question

Three capacitors of capacitances 2 μ F , 5 μ F , 8 μ F are connected first in parallel combination and then in series combination, The ratio of their equivalent capacitances will be (A) 15: 1 (B) 20: 1 (C) 13: 1 (D) 12: 1

Tardigrade Admin · Accepted Answer

C P =2+5+8=15 μ F (1/ C s )=(1/2)+(1/5)+(1/8)=(20+8+5/40) C s =(40/33) ( C P / C S )=(15/40) × 33 ≈ (12/1)

Q. Three capacitors of capacitances $2 μ F$ , $5 μ F$ , $8 μ F$ are connected first in parallel combination and then in series combination, The ratio of their equivalent capacitances will be

$15 : 1$

$20 : 1$

$13 : 1$

$12 : 1$

$C_{P} = 2 + 5 + 8 = 15 μ F$
$\frac{1}{C _{s}} = \frac{1}{2} + \frac{1}{5} + \frac{1}{8} = \frac{20 + 8 + 5}{40}$
$C_{s} = \frac{40}{33}$
$\frac{C _{P}}{C _{S}} = \frac{15}{40} \times 33$
$\approx \frac{12}{1}$

Q. Three capacitors of capacitances 2μF , 5μF, 8μF are connected first in parallel combination and then in series combination, The ratio of their equivalent capacitances will be

15:1

20:1

13:1

12:1