Question

A capacitor of capacitance 20 uF is charged to a potential of 500 V.
Calculate the charge and energy stored in a capacitor.
for​

Answer 1

Given:

A capacitor of capacitance, C= 20uF

and it's charged to a potential, V = 500 V

To Find :

• Charge
• Energy stored in a capacitor

Theory :

A capacitor is a device that stores electrical energy.

• Capacitance :

It is a measure of ability of the capacitor to store charge on it .

• Charge given to the conductor

$\bf\:Q=CV$

• Energy Stored in a charged capacitor

$\rm\:U=\dfrac{Q^2}{2C}=\dfrac{1}{2}CV^2=\dfrac{1}{2}QV$

Solution:

We have :

$\sf\:Capacitance,C=20\mu\:F=20\times10^{-6}F$

$\sf\:Potential,V=500V$

$\sf\:Charge,Q=?$

We know that

$\rm\green{Charge=Capacitance\times\:Potential}$

$\sf\implies\:Q=CV$

$\sf\implies\:Q=20\times10^{-6}\times500$

$\sf\implies\:Q=10\times10^{-3}$

$\sf\implies\:Q=10mC$

Now ,

Energy stored in a capacitor

$\rm\:U=\dfrac{1}{2}QV$

Put given values then ,

$\sf\implies\:U=\dfrac{1}{2}\times10\times500\times10^{-3}$

$\sf\implies\:U=\dfrac{1}{2}\times10^{3}\times5\times10^{-3}$

$\sf\implies\:U=\dfrac{1}{2}\times10^{(3-3)}\times5$

$\sf\implies\:U=\dfrac{5}{2}$

$\sf\implies\:U=2.5J$

_____________

More About the topic :

1. Capacitance is a scalar quantity
2. SI unit of capacitance is Farad (F)
3. Dimensions $\sf\:[M^{-1}L^{-2}T^{4}A^{2}]$

Answer 2

Answer:

Given:

A capacitor of capacitance, C= 20uF

and it's charged to a potential, V = 500 V

To Find :

Charge

Energy stored in a capacitor

Theory :

A capacitor is a device that stores electrical energy.

• Capacitance :

It is a measure of ability of the capacitor to store charge on it .

• Charge given to the conductor

\bf\:Q=CVQ=CV

• Energy Stored in a charged capacitor

\rm\:U=\dfrac{Q^2}{2C}=\dfrac{1}{2}CV^2=\dfrac{1}{2}QVU=

2C

Q

2

=

2

1

CV

2

=

2

1

QV

Solution:

We have :

\sf\:Capacitance,C=20\mu\:F=20\times10^{-6}FCapacitance,C=20μF=20×10

−6

F

\sf\:Potential,V=500VPotential,V=500V

\sf\:Charge,Q=?Charge,Q=?

We know that

\rm\green{Charge=Capacitance\times\:Potential}Charge=Capacitance×Potential

\sf\implies\:Q=CV⟹Q=CV

\sf\implies\:Q=20\times10^{-6}\times500⟹Q=20×10

−6

×500

\sf\implies\:Q=10\times10^{-3}⟹Q=10×10

−3

\sf\implies\:Q=10mC⟹Q=10mC

Now ,

Energy stored in a capacitor

\rm\:U=\dfrac{1}{2}QVU=

2

1

QV

Put given values then ,

\sf\implies\:U=\dfrac{1}{2}\times10\times500\times10^{-3}⟹U=

2

1

×10×500×10

−3

\sf\implies\:U=\dfrac{1}{2}\times10^{3}\times5\times10^{-3}⟹U=

2

1

×10

3

×5×10

−3

\sf\implies\:U=\dfrac{1}{2}\times10^{(3-3)}\times5⟹U=

2

1

×10

(3−3)

×5

\sf\implies\:U=\dfrac{5}{2}⟹U=

2

5

\sf\implies\:U=2.5J⟹U=2.5J

_____________

More About the topic :

Capacitance is a scalar quantity

SI unit of capacitance is Farad (F)

Dimensions \sf\:[M^{-1}L^{-2}T^{4}A^{2}][M

−1

L

−2

T

4

A

2

]