Question

a capacitor charged from a 50 v d.c supply found to have a charge of 10 microcoloumb. what is the capacitance of the capacitor and how much energy is stored in it

Answer 1

Hi dear friend, :)

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Firstly we need to refresh some ground concepts before answering the question(s);

i) A capacitor stores charge

ii) Charge flows to the capacitor from the emf device till the capacitor reaches its full potential(i.e; its charge to capacitance ratio) , and then it attains steady state where no more current flows from the power source.

iii) As the capacitor gains charge (stores the charge) it is said to posses electrical energy.

> Fromulae :

  1) q = vc

     q : the charge on the capacitor

     v : potential

     c : capacitance

2) energy of a capacitor :

 E =  1/2 cv²   {most used}

(or)

E=  $\frac{1}{2} qv$  

(or)

E=  $\frac{q^{2}}{2c}$  

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Now coming to the question,

c = q/v

∴ c =    (10 x 10^{-6} ) / 50

⇒c = 2 x 10^{-7}

and

E= 1/2 cv²

⇒ E= 1/2 x 2 x 10^{-7} x 25 x 10²

⇒ E = 2.5 x 10^{-4} [ Ans.]

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Cheers ;)