A capacitor of capacitance $900\, \mu F$ is charged by a $100\, V$ battery The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor The loss of energy in this process is measured as $x \times 10^{-2} J$ The value of $x$ is ______
Common potential will be developed across both capacitors by kVL
Total charge on left plates of capacitors should be conserved. ∴90mc+0=2cv0 cv0=45mc
Heat dissipated =Ui−Uf [Change in energy stored in the capacitors] =21900μF(90mc)2−2×21900μF(45mc)2[U=2cQ2] =2×900×10−61(8100−4050)×10−6 =2.25 Joule
OR Heat =21C1+C2C1C2(V1−V2)2 =212CC2(100−0)2 =212900×10−6×104=49 Joule =2.25 Joule
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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.
