Two capacitors of capacitances $C_1$ and $C_2$ are connected across $200 \,V$ power supply. The potential drop across $C_1$ is $120\, V. A$ capacitor of capacitance $2\,\mu F$ is connected in parallel with $C_1$ and the potential drop across $C_2$ becomes $160\, V$. What are the values of $C_1$ and $C_2$ in $\mu F$ ?
- 0.4 and 0.6
- 0.6 and 0.4
- 0.8 and 1.2
- 1.2 and 0.8
The Correct Option is A
Solution and Explanation
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Read the following paragraphs and answer the questions that follow:
A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges \( Q \) and \( -Q \) with a potential difference \( V = V_1 - V_2 \) between them. The ratio \( \frac{Q}{V} \) is a constant, denoted by \( C \), and is called the capacitance of the capacitor. It is independent of \( Q \) or \( V \). It depends only on the geometrical configuration (shape, size, separation) of the two conductors and the medium separating the conductors.
When a parallel plate capacitor is charged, the electric field \( E_0 \) is localized between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (charge density \( \sigma \)), the dielectric is polarized by the field. Consequently, opposite charges appear on the faces of the slab, near the plates, with surface charge density of magnitude \( \sigma_p \). For a linear dielectric, \( \sigma_p \) is proportional to \( E_0 \). Introduction of a dielectric changes the electric field, and hence, the capacitance of a capacitor, and hence, the energy stored in the capacitor. Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel.- CBSE CLASS XII - 2025
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Concepts Used:
Capacitor
Capacitors commonly known as Condensers are passive components, similar to a resistor. In capacitors, charges are usually stored in the form of an "electrical field". Electrical and electronic circuits depend on the same which is made up of two parallel metal plates that are not connected to one another. The two plates are separated by a non-conducting insulating medium called dielectric.
Uses of Capacitors:
- DC blocking capacitors block the DC and allows only AC to certain parts of the circuit.
- These are main elements of filters.
- They possess the ability to couple a section of the circuit to another.
Types of Capacitors:
- Ceramic capacitors are created by covering two sides of their tiny ceramic disc with silver and stacking them together.
- Film Capacitors are commonly used capacitors that are made up of different sets of capacitors.
- In an electrolytic capacitor metallic anode coated with an oxidized layer used as a dielectric.
- A Paper capacitor is also known as a fixed capacitor in which paper is used as the dielectric material.
Read More: Types of Capacitors