Capacitance of Parallel Plate Capacitor

A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by $T=2\pi \sqrt{\frac{l}{g^{\prime }}}$ , where g is equal to

1. g

2. g-a

3. g+a

4. 

1. Decreases
2. Does not change
3. Becomes zero

4. Increases

A capacitor $C$ is fully charged with voltage $V_0$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C/2. The energy loss in the process after the charge is distributed between the two capacitors is:

1. $\frac{1}{2}C{V_0}^2$

2. $\frac{1}{4}C{V_0}^2$

3. $\frac{1}{3}C{V_0}^2$

4. $\frac{1}{6}C{V_0}^2$

1. $10\text{mA}$
2. $30\text{mA}$
3. $40\text{mA}$
4. $20\text{mA}$

1. Zero
2. $\frac{\sigma \lambda l^2}{8{ϵ}_0}\sin \theta$
3. $\frac{\sigma \lambda l^2}{{ϵ}_0}\sin \theta$
4. $\frac{\sigma \lambda l^2}{2{ϵ}_0}$

1. $1\mu \text{F}$
2. $2\mu \text{F}$
3. $4.2\mu \text{F}$
4. $9.2\mu \text{F}$

1. 4
2. 2
3. 3
4. 1

A composite slab consists of two slabs A and B of different materials but of the same thickness placed one on top of the other. The thermal conductivities of A and B are $k_{1}and{k}_2$ respectively. A steady temperature difference of ${12}^{\circ }C$ is maintained across the composite slab. If $k_1=\frac{k_2}{2}$, the temperature

A parallel-plate capacitor has plate area $25.0c{m}^2$ and a separation of 2.00 mm between the plates. The capacitor is connected to a battery of 12.0 V. (a) Find the charge on the capacitor. (b) The plate separation is decreased to 1.00 mm. Find the extra charge given by the battery to the positive plate.

1. $\frac{2}{5}\frac{{\epsilon }_{0}A}{d}$
2. $\frac{5}{2}\frac{{\epsilon }_{0}A}{d}$
3. $\frac{3}{2}\frac{{\epsilon }_{0}A}{d}$
4. $\frac{{\epsilon }_{0}A}{d}$

1. Charge
2. Potential difference
3. Size of the plates
4. Separation between the plates

1. $\frac{C}{C_1}=\frac{2+K}{K}$
2. $\frac{E_1}{E_2}=\frac{1}{K}$
3. $\frac{Q_1}{Q_2}=\frac{3}{K}$
4. $\frac{E_1}{E_2}=1$

1. $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{R^2}\text{for}r<R$
2. $\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{R^2}>F>0\text{for}r<R$
3. $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r^2}\text{for}r>R$
4. $F=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{R^2}\text{for all}r$

Two small charged spheres A and B have charges of $10\text{μC}$ and $40\text{μC}$ respectively and are held at a separation of $90\text{cm}$ from each other. At what distance from A, electric field intensity would be zero?

1. $22.5\text{cm}$

2. $18\text{cm}$

3. $30\text{cm}$

4. $36\text{cm}$