Question

In the circuit shown, the switch S1​ is closed for long time and at \[t = 0s\], the switch S2 is closed and S1​ is opened simultaneously. What is the maximum charge (in the unit of \[\mu C\]) on the \[4\mu F\] capacitor?
  

Answer 1

Hint: Charging of a capacitor is defined as when the electrical energy is added to it is called charging while discharging is defined as releasing the energy from the capacitor. Use the formula of Current to find its value and then substitute its value in the formula of Energy in the Inductor to get the Answer.

Complete step by step answer:
When the switch \[{S_1}\] is closed, the voltage entirely drops across the \[20\Omega \] resistor.
Now,
In the Circuit, the current is
\[i = \dfrac{V}{R} = \dfrac{{1.5}}{{20}} = 0.075amp\]
We know that,
Energy in the inductor is given by \[U = \dfrac{1}{2}L{i^2}\]
When \[{S_1}\] is opened and \[{S_2}\]is closed, when the charge on the capacitor is maximum, max energy in the capacitor will be stored
Thus, \[\dfrac{1}{2}L{i^2} = \dfrac{1}{2}\dfrac{{{q^2}_{\max }}}{C}\]
\[{q_{\max }} = \sqrt {LC{i^2}} \]
\[ = 0.075 \times \sqrt {0.4 \times {{10}^{ - 3}} \times (4 \times {{10}^{ - 6}})} \]
\[ = 4 \times {10^{ - 5}} \times 75 \times {10^{ - 3}}\]
\[ = 3 \times {10^{ - 6}} = 3\mu C\]
The capacitor is a device which has the ability to store an electric charge across its plates. It is made of two parallel conducting metal plates separated through a distance. These are separated by an insulating material called dielectric. The dielectric can be paper, glass, air, plastic etc. Capacitors have many important applications in electronics and they vary in shape and size. When the Voltage across its plates equals the supply voltage, then the Capacitor is said to be fully charged.

Note:
The charge on the capacitor (Q) is directly proportional to the potential difference (V) between the plates i.e \[Q\alpha V\]
Capacitors are used for multiple purposes-
- It is used for Filtering out unwanted frequency signals.
- Storing electric potential energy such as batteries.
- Used as a sensing device.
- Used in the audio system of the vehicle.
- Used to separate AC and DC.
Resistors are electrical devices that oppose the flow of current when it flows through them. Voltage defines the potential difference between two points in the given electrical circuit. The voltage is measured in volt.