What will be the equivalent capacitance ?

1 )   what will be the equivalent capacitance ?

A ) 1.5 C ,                                         B )  1 C ,

C )  2 C ,                                           D ) None of these ,

Correct Answer : -   B )  1 C ,

Solution : -

Formulas : -

Capacitance in series : -      1/Cs = 1/C₁+ 1/C₂ + 1/C₃ + ……………… ,

Capacitance in parallel : -    Cp = C₁ + C₂+ C₃ + ……………… ,

So ,

Cp = 2C + 2C = 4C ,

So ,  we have 

So ,          1/Ce = 1/4C + 1/2C + 1/4C  ,

Therefore ,    Ce = 1C ,     Answer .

 

2 )  The capacitance of parallel plate capacitor is ................  ( C = (kA£_o)/d ) .

 

3 ) In parallel plate capacitor , what would be new capacitance if separation (d) is double and area in halved ?

A ) Becomes double ,                                 B )  Remain same ,

C ) Become one – forth ,                             D ) None of these ,

Correct Answer : -   C ) Become one – forth ,

Solution : -

Formula : - 

For parallel plate capacitor  ,  capacitance is :- 

C =  ( kA£_o ) / d  .

If separation between slits become double  ,  dʹ = 2 d  ,

And area become half ,     Aʹ = A / 2 ,

 So ,   

Ø    Cʹ =   ( kAʹ£_o ) / dʹ  .

Ø    Cʹ =   k(A / 2)£_o  / 2d .

Ø    Cʹ =   ( kA£_o ) / 4d .   ,   So ,

Ø    Cʹ =   C / 4    ,     Answer .

 

4 )   If current is increased by 100 times. What would be effect on energy stored in inductor?

A ) increase by 1000 times ,                        B ) increase by 10000 times ,

C ) No change  ,                                D ) None of these ,

Correct Answer : -   B ) increase by 10000 times ,

Solution : -

Formula : -

Energy stored in inductor : -

E =  (1/2)L(I)^2  ,

·         I = current in inductor  ,

·         L = self inductance ,

So ,   if  current is increased by 100 times ,    Iʹ = 100 I  ,

So  energy stored in inductor will be : -

Ø  Eʹ =  (1/2)L(Iʹ)^2  ,

Ø  Eʹ =  ( 1 / 2 ) * L * ( 100 I )^2  ,

Ø  Eʹ =  ( 1 / 2 ) * L * ( 10000 I^2 ) =  (10000)(1/2)LI^2  ,

Ø  Eʹ = ( 10000 ) * E .    Answer .

SO , it will increased by ten thousand times . 

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