
What is the dimensional formula of capacitance?
Answer
523.5k+ views
Hint: Capacity is a system 's capability to store an electrical charge. It is given by the ratio of the increase in a system's electrical charge to the corresponding change in its electrical potential.
Complete step-by-step answer:
Capacitors consist of two parallel conductive plates, usually metal, which are prevented from touching each other and separated by a dielectric insulating layer. When an electrical current flow is applied to these pipes, charging one surface with a positive charge and the other plate with an equal and opposite negative charge proportional to the supply voltage. A condenser has the capacity to store an electrical charge Q of electrons.
The capacitor capacity to store this electric charge Q between its plates is proportional to the voltage V applied to a capacitor.
It can also be written as
Capacitance, C= Charge ---(i)
We know, Charge = Current Time
Dimensional formula of charge is ---(ii)
Voltage = Electric Field Distance ---(iii)
Also, Electric field = Force
The dimensional formula of force and charge is given by
dimensional formula of charge is given by
Hence the dimensional formula for Electric field is
= --(iv)
In substituting (iv) and (iii) we get,
The dimensional formula of Voltage= = ---(v)
On substituting equation (v) and (ii) in equation (i) we get,
Capacitance = Charge
Hence, C= =
Therefore, the Capacitance is dimensionally represented as
Note: Once a condenser is fully charged, there is a possible difference between the plates and the greater the area of the plates or the greater the distance between them, the greater the capacitance of the condenser.
Complete step-by-step answer:
Capacitors consist of two parallel conductive plates, usually metal, which are prevented from touching each other and separated by a dielectric insulating layer. When an electrical current flow is applied to these pipes, charging one surface with a positive charge and the other plate with an equal and opposite negative charge proportional to the supply voltage. A condenser has the capacity to store an electrical charge Q of electrons.
The capacitor capacity to store this electric charge Q between its plates is proportional to the voltage V applied to a capacitor.
It can also be written as
Capacitance, C= Charge
We know, Charge = Current
Dimensional formula of charge is
Voltage = Electric Field
Also, Electric field = Force
The dimensional formula of force and charge is given by
dimensional formula of charge is given by
Hence the dimensional formula for Electric field is
=
In substituting (iv) and (iii) we get,
The dimensional formula of Voltage=
On substituting equation (v) and (ii) in equation (i) we get,
Capacitance = Charge
Hence, C=
Therefore, the Capacitance is dimensionally represented as
Note: Once a condenser is fully charged, there is a possible difference between the plates and the greater the area of the plates or the greater the distance between them, the greater the capacitance of the condenser.
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