Discharging of Capacitors

Q.

If $n$ is the number of electrons that flow through a conductor in time $t$, write down the expression for the current flowing through the circuit.

Q. While charging/discharging a capacitor, there are charges moving towards/away from the capacitor which ensures current flow in a circuit.

1. False
2. True

Q. A parallel plate capacitor of $1\mu F$ capacity is discharging through a resistor. If its energy reduces to half in one $\text{second}$. The value of resistance will be

1. $\frac{2}{ln\left(2\right)}M\Omega$
2. $\frac{4}{ln\left(2\right)}M\Omega$
3. $\frac{10}{ln\left(2\right)}M\Omega$
4. $\frac{16}{ln\left(2\right)}M\Omega$

Q. A series $LCR$ circuit driven by $300\text{V}$ at a frequency of $50\text{Hz}$ contains a resistance $R=3k\Omega$, an inductor of inductive reactance $X_L=250\pi \Omega$ and an unknown capacitor. The value of capacitance, to maximize the average power, should be:$\text{Take}({\pi }^2\approx 10)$

1. $400\mu \text{F}$
2. $25\mu \text{F}$
3. $4\mu \text{F}$
4. $40\mu \text{F}$

Q. A parallel plate capacitor of $1\mu F$ capacity is discharging through a resistor. If its energy reduces to half in one $\text{second}$. The value of resistance will be

1. $\frac{2}{ln\left(2\right)}M\Omega$
2. $\frac{4}{ln\left(2\right)}M\Omega$
3. $\frac{10}{ln\left(2\right)}M\Omega$
4. $\frac{16}{ln\left(2\right)}M\Omega$

Q. In the circuit shown there is steady state with the switch closed. The switch is opened at $t=0$. Choose the correct option(s). (Given : $\epsilon =24\text{V},C_1=3\text{F}$ and $C_2=2\text{F})$

1. The voltage across $C_1$ before the switch is open is $12\text{V}$.
2. The voltage across $C_1$ after the switch is open for a long time is $12\text{V}$.
3. The voltage across $C_2$ after the switch is open for a long time is $24\text{V}$.
4. The voltage across $C_2$ before the switch is open is $8\text{V}$.