More about Q=CV

Q. The linear charge density of a thin rod of length $l$ varies with the distance $x$ from the left-most end as $\lambda ={\lambda }_0{x}^2(0\le x\le l)$. The total charge on the rod is

1. $\frac{{\lambda }_0{l}^3}{3}$
2. $\frac{{\lambda }_0{l}^2}{3}$
3. $\frac{2{\lambda }_0{l}^2}{3}$
4. $\frac{{\lambda }_0{l}^3}{4}$

Q. Three capacitors each of $3\mu \text{F}$ are connected in a circuit. The maximum and minimum equivalent capacitance that can be obtained using these capacitors are

1. $9\mu \text{F},1\mu \text{F}$
2. $3\mu \text{F},2\mu \text{F}$
3. $8\mu \text{F},2\mu \text{F}$
4. $9\mu \text{F},0\mu \text{F}$

Q. A parallel-plate capacitor is constructed using three different dielectric materials as shown in the figure. What is the capacitance across P and Q?

1. $(\frac{K_1}{2}+\frac{K_2{K}_3}{K_2+K_3})\frac{{\epsilon }_{0}A}{t}$
2. $(K_1+\frac{K_2{K}_3}{K_2+K_3})\frac{{\epsilon }_{0}A}{t}$
3. $(K_1+\frac{2K_2{K}_3}{K_2+K_3})\frac{{\epsilon }_{0}A}{t}$
4. $(K_1+\frac{K_2{K}_3}{2(K_2+K_3)})\frac{{\epsilon }_{0}A}{t}$

Q.

Two insulated charged spheres of radii 20cm and 25cmrespectively and

having an equal charge Q are connected by a copper wire, then they are

separated

1. Both the spheres will have the same charge Q

2. Charge on the 20cm sphere will be greater than that on the 25cm sphere

3. Charge on the 25cm sphere will be greater than that on the 20cm sphere

4. Charge on each of the sphere will be 2Q

Q. For any randomly shaped conductor, Q is proportional to V.

1. False
2. True

Q. A $5\mu \text{F}$ capacitor is charged fully by a $220\text{V}$ supply. It is then disconnected from the supply and is connected across another uncharged $2.5\mu \text{F}$ capacitor. If the energy change during the charge redistribution is $\frac{X}{100}\text{J}$ then the value of $X$ to the nearest integer is

Q. Two parallel plate capacitors $\text{A}$ and $\text{B}$ having capacitance $2\mu \text{F}$ and $3\mu \text{F}$ are charged separately up to $20\text{V}$ and $10\text{V}$ respectively. Now, the positive plate of $\text{A}$ is connected to the positive plate of $\text{B}$ and negative plate of $\text{A}$ is connected with negative plate of $\text{B}$. Find how much charge flows in the circuit?

1. $40\mu \text{C}$
2. $42\mu \text{C}$
3. $12\mu \text{C}$
4. $28\mu \text{C}$