
The charge in the capacitor at steady state is
A. Zero
B.
C.
D.

Answer
440.4k+ views
Hint:In order to answer the above question, we will first of all discuss a capacitor and its steady state. Secondly, we will observe the circuit and draw the resultant circuit for a steady capacitor. Finally using Kirchhoff’s law, we will derive the voltage across the capacitor and the charge stored on the capacitor.
Formula used:
Kirchhoff’s Loop Rule:
Where is voltage.
Capacitance of a capacitor:
Where is the capacitance, is the charge and is the voltage across the capacitor.
Complete step by step answer:
A capacitor is a two-terminal electrical component that can store energy in the form of an electric field. It is made up of two electrical conductors separated by a certain distance. The gap between the conductors can be filled with vacuum or a dielectric, which is an insulating material. Capacitance refers to the capacitor's capacity to store charges.
Capacitors store energy by separating opposing charge pairs. A parallel plate capacitor is the most basic design, consisting of two metal plates separated by a gap. However, capacitors come in a variety of shapes, sizes, heights, and girths, as well as a variety of materials.
When a capacitor is attached to a circuit, it starts charging. After the capacitor has fully charged, the current flowing through the capacitor will stop. Hence, when there is no current flowing through it, the capacitor will behave as an open circuit and it is said to be in steady state.
Now, if we look at the question, the capacitor having a capacity of is said to be a steady capacitor. Therefore, the above circuit can be shown as
Here, the capacitor behaves as an open in the circuit. Now, if we consider the loop and apply Kirchhoff’s law, we get
Now, we know that the potential across the capacitor is shown by and . Therefore, the potential difference across the capacitor is given as
Considering the loop and using the Kirchhoff’s law, we get
Using the result from above calculation and taking , we get
Thus, it can be said that the potential difference across the capacitor is zero.
As we know that the capacitance of the capacitor is given by the equation
The capacitance of the capacitor is given as in the question. Thus, placing the values of and , we get
According to the equation above, it is proved that the charge stored on the capacitor is also zero as the potential difference across the capacitor is zero.
Hence, the correct answer is option A.
Note:It is very important to note that the capacitor can only be in a steady state when no amount of current is flowing through it. The first case is when the capacitor is fully charged. But we can see from our answer that the charge on the capacitor is zero. Hence, the capacitor hasn't charged at all. What does this mean? It means that in the above circuit, the capacitor faces the same potential difference which is opposite to each other on both the plates and it cancels out each other. i.e.
The voltage due to battery in addition to the resistor = - (the voltage due to the battery)
Therefore, the capacitor becomes neutral and no current flows through it and it remains discharged.
Formula used:
Kirchhoff’s Loop Rule:
Where
Capacitance of a capacitor:
Where
Complete step by step answer:
A capacitor is a two-terminal electrical component that can store energy in the form of an electric field. It is made up of two electrical conductors separated by a certain distance. The gap between the conductors can be filled with vacuum or a dielectric, which is an insulating material. Capacitance refers to the capacitor's capacity to store charges.
Capacitors store energy by separating opposing charge pairs. A parallel plate capacitor is the most basic design, consisting of two metal plates separated by a gap. However, capacitors come in a variety of shapes, sizes, heights, and girths, as well as a variety of materials.
When a capacitor is attached to a circuit, it starts charging. After the capacitor has fully charged, the current flowing through the capacitor will stop. Hence, when there is no current flowing through it, the capacitor will behave as an open circuit and it is said to be in steady state.
Now, if we look at the question, the capacitor having a capacity of

Here, the capacitor behaves as an open in the circuit. Now, if we consider the loop
Now, we know that the potential across the capacitor is shown by
Considering the loop
Using the result from above calculation
Thus, it can be said that the potential difference across the capacitor is zero.
As we know that the capacitance of the capacitor is given by the equation
The capacitance of the capacitor is given as
According to the equation above, it is proved that the charge stored on the capacitor is also zero as the potential difference across the capacitor is zero.
Hence, the correct answer is option A.
Note:It is very important to note that the capacitor can only be in a steady state when no amount of current is flowing through it. The first case is when the capacitor is fully charged. But we can see from our answer that the charge on the capacitor is zero. Hence, the capacitor hasn't charged at all. What does this mean? It means that in the above circuit, the capacitor faces the same potential difference which is opposite to each other on both the plates and it cancels out each other. i.e.
The voltage due to
Therefore, the capacitor becomes neutral and no current flows through it and it remains discharged.
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