Capacitors and Dielectrics

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Question
ICSEENIPH12029750

The particles which cannot be accelerated by a cyclotron or a Van de Graff generator are :
  • Alpha particles 
  • Beta particles
  • Neutrons   
  • Protons

Solution

C.

Neutrons   

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Question
ICSEENIPH12029768

Three capacitors C1 = 6μF,C2 = 12μF and C3 = 20μF are connected to a 100 V battery, as shown in Figure 2 below :

Calculate:

(i) Charge on each plate of capacitor Cx
 
ii) Electrostatic potential energy stored in capacitor C3.

 

Solution

i)
Equivalent of C1 and C2 is
straight C space equals space fraction numerator 6 space straight x space 12 space straight x space 10 to the power of negative 6 end exponent over denominator 18 end fraction space equals space 4 space cross times space 10 to the power of negative 6 end exponent space straight F

straight Q space equals space CV

straight Q space equals space 4 space straight x space 10 to the power of negative 6 end exponent space straight x space 100 space equals space 400 space straight x space 10 to the power of negative 6 end exponent space straight C

straight Q subscript 1 space equals space straight Q subscript 2 space equals space 400 space straight x space 10 to the power of negative 6 end exponent space straight C 
ii)
Energy on capacitor C

straight E space equals space 1 half straight C subscript 3 space straight V squared space equals space 1 half straight x 20 cross times 10 to the power of negative 6 end exponent space straight x space left parenthesis 100 right parenthesis squared equals space 0.1 space straight J

Question
ICSEENIPH12029862

Three capacitors each of capacitance C are connected in series. Their equivalent capacitance is Cs. The same three capacitors are now connected in parallel. Their equivalent capacitance becomes CP find the ratio open parentheses straight C subscript straight P over straight C subscript straight S close parentheses

Solution

Capacitors each of capacitance C.

Series capacitance = Cs.

Parallel capacitance = Cp.

Cp= C + C + C = 3C
1 over straight C subscript straight S space equals space 1 over C space plus space 1 over C space plus space 1 over C

1 over straight C subscript straight S space equals 3 over straight C

straight C subscript straight S space equals space straight C over 3
Now comma space

straight C subscript straight P over straight C subscript straight S space equals space fraction numerator 3 straight C over denominator straight c divided by 3 end fraction space equals space 9

Question
ICSEENIPH12029908

An isolated 16 μF parallel plate air capacitor has a potential differences of 1000 V (Figure 5 a). A dielectric slab having relative permittivity (i.e. dielectric constant) = 5 is introduced to fill the space between the two plates com pletely. (Figure 5 b). Calculate:

(i) The new capacitance of the capacitor.

(ii) The new potential differences between the two plates of the capacitor



Solution

C1 = 16 μ F    where C1 → Capacitance of figure 5(a)

V1= 1000 V    C2 → Capacitance of figure 5 (b)

(i) C2 / C1 = K

C2 = K C1 

    = 5 X 16 
    = 80 μF, is the new capacitance of the capacitor.

(ii) Similarly V2 / V1 = 1/K

rightwards double arrow V2 = V1 / K
         = 1000 / 5

         = 200 V.