Question

If ‘n’ capacitors each of capacitance C are connected in series with a battery of V volts. What will be the effect on the equivalent capacitance and the total energy stored in the combination when compared to the capacitance and energy stored in a single capacitor of capacitance C. ​

Answer 1

Answer:

total capacitance decreases and energy stored also decreases

Answer 2

Given:

‘n’ capacitors each of capacitance C are connected in series with a battery of V volts.

To find:

Effectan equivalent capacitance and Total energy stored in the combination when compared to a single capacitor

Calculation:

For the combination:

Net Capacitance be C_{net}.

$\sf{ \therefore \: \dfrac{1}{C_{net}} = \dfrac{1}{C} + \dfrac{1}{C} + ..... \: n \: times}$

$\sf{ = > \: \dfrac{1}{C_{net}} = \dfrac{n}{C} }$

$\boxed{ \sf{ = > \: C_{net} = \dfrac{C}{n} }}$

So, net capacitance is 1/n times the capacitance of a single capacitor.

Total Energy stored ;

$\therefore \: \sf{E_{net} = \dfrac{1}{2} C_{net} {(volt)}^{2} }$

$= > \: \sf{E_{net} = \dfrac{1}{2}( \dfrac{C}{n}){(volt)}^{2} }$

$= > \: \sf{E_{net} = \dfrac{C{(volt)}^{2} }{2n}}$

So, net energy stored will be 1/n times the energy of a single capacitor.