Capacitors and combinations in series and parallel — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The capacitance of an isolated capacitor is defined by

• A. $C=Q/V$
• B. $C=QV$
• C. $C=V/Q$
• D. $C=Q^2/V$

Question 2 · difficulty L2 · understanding

A capacitor $P$ with capacitance $10 \times 10^{-6} \mathrm{~F}$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20 \times 10^{-6} \mathrm{~F}$. The charge on capacitor $Q$ when equilibrium is established will be $\alpha \times 10^{-5} C$ (assume capacitor $Q$ does not have any charge initially), the value of $\alpha$ is $\_\_\_\_$ .

Question 3 · difficulty L2 · understanding

A capacitor of capacitance $$\mathrm{C}$$ and potential $$\mathrm{V}$$ has energy $$\mathrm{E}$$. It is connected to another capacitor of capacitance $$2 \mathrm{C}$$ and potential $$2 \mathrm{~V}$$. Then the loss of energy is $$\frac{x}{3} \mathrm{E}$$, where $$x$$ is _______.

Question 4 · difficulty L2 · understanding

In the given figure the total charge stored in the combination of capacitors is $100~ \mu \mathrm{C}$. The value of ' $x$ ' is _________.

Question 5 · difficulty L2 · understanding

The equivalent capacitance between points A and B in below shown figure will be __________ $$\mu$$F.

Question 6 · difficulty L2 · understanding

A 2$$\mu$$F capacitor C 1 is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C 2 of 8 $$\mu$$F. The charge in C 2 on equilibrium condition is ____________ $$\mu$$C. (Round off to the Nearest Integer)

Question 7 · difficulty L2 · understanding

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V , its capacitance is: (in pF )

• A. 600
• B. 100
• C. 400
• D. 200

Question 8 · difficulty L2 · understanding

A capacitor, $C_1 = 6 \mu F$ is charged to a potential difference of $V_0 = 5V$ using a 5V battery. The battery is removed and another capacitor, $C_2 = 12 \mu F$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached.

• A. $q_1 = 10 \mu C, \ q_2 = 20 \mu C$
• B. $q_1 = 15 \mu C, \ q_2 = 30 \mu C$
• C. $q_1 = 20 \mu C, \ q_2 = 10 \mu C$
• D. $q_1 = 30 \mu C, \ q_2 = 15 \mu C$

Question 9 · difficulty L2 · understanding

Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor $R$. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below:

• A. A, C Only
• B. C, D Only
• C. A, B, D Only
• D. B, C, D Only

Question 10 · difficulty L2 · understanding

Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and $C$ stand for unit of mass, length, time and charge,

• A. $[\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
• B. $[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]$
• C. $[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
• D. $[\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]$