Two metal plate form a parallel plate capacitor. The distance between the plates is $d$. A metal sheet of thickness $d/2$ and of the same area is introduced between the plates. What is the ratio of the capacitances in the two cases?
The capacitance of the air filled parallel plate capacitor is given by $C = \frac{\varepsilon_0 A}{d} $ ....(i) When a slab of dielectric constant $K$, and thickness $t$ is introduced in between the plates of the capacitor, its new capacitance is given by, $C' = \frac{\varepsilon_0 A}{d - t \left( 1 - \frac{1}{K} \right)}$ Since a metal sheet of thickness $d/2$ is introduced, hence here, $t = d/2, K = 8$ (for metals) or $\frac{1}{K} = 0$ $\therefore \:\:\: C' = \frac{ \varepsilon_0 A}{d - \frac{d}{2}} = \frac{ 2\varepsilon_0 A}{d}$ .....(ii) Hence, from eqs. (i) and (ii), we get $\therefore \:\:\:\:\frac{C'}{C} = \frac{\frac{2 \varepsilon_{0}A}{d}}{\frac{ \varepsilon_{0}A}{d}} = \frac{2}{1} =2 :1$
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Top Questions on electrostatic potential and capacitance
The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.
Some major things that we should know about electric potential:
They are denoted by V and are a scalar quantity.
It is measured in volts.
Capacitance
The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.
The capacitor is in Series and in Parallel as defined below;
In Series
Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitor’s capacitance.
In Parallel
Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitor’s capacitance.
