First slide

Capacitors and capacitance

Question

Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is 10 $μ$ F. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor $C_{2}$ is 4 times that of $C_{1}$ . If these capacitors are connected in series, their effective capacitance will be:

Easy

A

1.6 $μ$ F
B

3.2 $μ$ F
C

8.4 $μ$ F
D

4.2 $μ$ F

Solution

Given : Capacitors connected in parallel : $C_{1} + C_{2} = 10 μ F ........ (i)$
$N o w, t h e y a r e c o n n e c t e d i n d i v i d u a l l y t o s a m e v o l t a g e s o u r c e . ∴ 4 \times E n e r g y i n C_{1} = E n e r g y i n C_{2} \Rightarrow 4 (\frac{1}{2} C_{1} V^{2}) = \frac{1}{2} C_{2} V^{2}$
$\Rightarrow 4 C_{1} = C_{2} ........ (i i)$
from equation (i) & (ii)
$C_{1} = 2 μ F C_{2} = 8 μ F$
If they are in series $C_{e q .} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{2 \times 8}{2 + 8} = 1.6 μ F$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App