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Question: An air capacitor of capacity \(c=10\mu F\) is connected to a constant voltage battery of 12 volt. No...

An air capacitor of capacity c=10μFc=10\mu F is connected to a constant voltage battery of 12 volt. Now the space between the plates is filled with a liquid of dielectric constant55. The additional charge that flows now from battery to the capacitor is:
A.120μC B.600μC C.480μC D.24μC \begin{aligned} & A.120\mu C \\\ & B.600\mu C \\\ & C.480\mu C \\\ & D.24\mu C \\\ \end{aligned}

Explanation

Solution

The basic equation of capacitor is used to solve this problem. A capacitor is used to store electric charges in between two dielectric materials which can be later used as a source of electric charge capacitor is widely used in the area of electronics.

Complete step by step answer:
First of all let us take a look at what a capacitor is.
A capacitor is a device which stores electrical energy in the electric field. It is a passive electronic device with two terminals.
The capacitance is the effect of a capacitor. When an amount of capacitance exists between any two electrical conductors in a circuit, the capacitor is the component designed to add capacitance to the circuit. The capacitor is also known as a condenser. Most capacitors include at least two electrical conductors sometimes in the form of metallic plates or surfaces which are separated by a dielectric medium.
In this question, it is given that,
c=10μF v=12V ε0=5 \begin{aligned} & c=10\mu F \\\ & v=12V \\\ & {{\varepsilon }_{0}}=5 \\\ \end{aligned}
As we all know, the charge store in a capacitor is given by the formula,
Q=CVQ=CV
Substituting the values in it, the initial charge,
Q1=CV=10×12=120μC{{Q}_{1}}=CV=10\times 12=120\mu C
After filling the dielectrics,
Qf=CfV{{Q}_{f}}={{C}_{f}}V
=KCV=5×10×12=600μC=KCV=5\times 10\times 12=600\mu C
Therefore the additional charge that flows from battery to the capacitor is
Qf−Qi=600−120=480μC{{Q}_{f}}-{{Q}_{i}}=600-120=480\mu C

Therefore the correct answer is option C.

Note:
A conductor can be a foil, thin film, sintered bead of metal, or an electrolyte. The dielectric acts to increase the charge capacity of a capacitor. Basically dielectric is nonconductive. Examples include glass, ceramic, plastic film, paper, mica, air, and oxide layers. Capacitors are commonly used as parts of electrical circuits in many daily useful electrical devices.