
A metal plate of thickness is introduced in between the plates of a parallel plate air capacitor with plate separation of . Capacity of the metal plate:
A. Decreases 2 times
B. Increases 2 times
C. Remains same
D. Becomes zero
Answer
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Hint: Use the formula for capacitance of the parallel plate capacitor. Also use the formula for capacitance of the parallel plate capacitor when a dielectric is introduced between the plates of the capacitor. Use the value of dielectric constant of the metal and substitute it in the formula for capacitance. Hence, determine the new value of the capacitance in terms of the initial capacitance.
Formulae used:
The capacitance of a parallel plate capacitor is given by
…… (1)
Here, is an area of the capacitor, is permittivity of free space and is separation between the two plates of the capacitor.
The capacitance of the parallel plate capacitor when a dielectric is introduced between the plates of the capacitor is
…… (2)
Here, is the area of capacitor, is permittivity of free space, is separation between the two plates of the capacitor, is thickness of the dielectric and is dielectric constant.
Complete step by step answer:
We have given that the separation between the two plates of a parallel plate air capacitor is .A metal plate of thickness is introduced between the two plates of the capacitor.
We have asked to calculate the new capacitance of the capacitor when the metal plate is introduced between the plates of the capacitor. Let be the initial capacitance of the capacitor and be the new capacitance of the capacitor.The initial capacitance of the parallel plate capacitor is given by
We know that the dielectric constant for the metal is infinite.
Let us now calculate the new capacitance of the capacitor after introduction of the metal plate using equation (2). Substitute for , for and for in equation (2).
Substitute for in the above equation.
Therefore, the new capacitance of the parallel plate capacitor will increase 2 times.
Hence, the correct option is B.
Note:One can also solve the same question by another method. One can use the concept that when the metal plate of given thickness is introduced between the plates of the capacitor, the charge on one plate of capacitor shifts on the introduced metal plate and the separation between the plates of capacitor decreases to a value decreased by the value equal to thickness of the introduced metal plate. This new separation distance gives the value of new capacitance.
Formulae used:
The capacitance
Here,
The capacitance
Here,
Complete step by step answer:
We have given that the separation between the two plates of a parallel plate air capacitor is
We have asked to calculate the new capacitance of the capacitor when the metal plate is introduced between the plates of the capacitor. Let
We know that the dielectric constant for the metal is infinite.
Let us now calculate the new capacitance of the capacitor after introduction of the metal plate using equation (2). Substitute
Substitute
Therefore, the new capacitance of the parallel plate capacitor will increase 2 times.
Hence, the correct option is B.
Note:One can also solve the same question by another method. One can use the concept that when the metal plate of given thickness is introduced between the plates of the capacitor, the charge on one plate of capacitor shifts on the introduced metal plate and the separation between the plates of capacitor decreases to a value decreased by the value equal to thickness of the introduced metal plate. This new separation distance gives the value of new capacitance.
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