Breaking a Capacitor into Combinations

Q. 6. Acircular plate of diameter a is kept in contact with a square plate of side a as shown. The density of the material and the thickness are samehere. The centre of mass of composite system will be -inside the circular plate -inside the square plate -at the point of contact -outside the sys

Q.

When a dielectric slab of thickness 6cm is introduced between the plates of parallel plate condenser, it is found that the distance between the plates has to be increased by 4cm to restore the capacity to original value. The dielectric constant of the slab is

1. 1.5
2. $\frac{2}{3}$
3. 3
4. 4

Q. In the circuit shown in the figure, initially the switch is open. When the switch is closed, the charge passing through the switch is

1. $600\mu \text{C}$; From $\text{B}$ to $\text{A}$
2. $60\mu \text{C}$; From $\text{A}$ to $\text{B}$
3. $120\mu \text{C}$; From $\text{B}$ to $\text{A}$
4. $120\mu \text{C}$; From $\text{A}$ to $\text{B}$

Q.
Find equivalent capacitance of system if plate area is $A$.
[Dielectric slab of constant $2K$ and $K$ are of same volume and half of the volume of the slab of constant $3K$.]

1. $\frac{5{ϵ}_{0}AK}{d}$
2. $\frac{13}{6}\frac{{ϵ}_{0}AK}{d}$
3. $\frac{6{ϵ}_{0}AK}{d}$
4. $\frac{15}{7}\frac{{ϵ}_{0}AK}{d}$

Q. The capacitance of a parallel plate air condenser is 2 $\mu$ F. A dielectric of constant 4 is introduced as shown in the figure to fill half the space between the parallel plates. Its capacitance now will be?

1. $20\mu F$
2. $3.2\mu F$
3. $5.0\mu F$
4. $6.4\mu F$

Q. I have multiple dielectrics (of surface area in contact with capacitor as $A_1,A_{2}and{A}_3)$ in my capacitor inserted as shown. What is my new capacitance?

1. $\frac{{\epsilon }_0}{d}(k_1+k_2+k_3)A$
2. $\frac{{\epsilon }_{0}d}{A}(k_1+k_2+k_3)$
3. $\frac{{\epsilon }_0}{d}(k_1{A}_1+k_2{A}_2+k_3{A}_3)$
4. $\frac{{\epsilon }_0}{d}(A_1+A_2+A_3)k_1$

Q. A piece of copper having a rectangular cross-section of $15.2mm\times 19.1mm$ is pulled in tension with $44,500N$ force, producing only elastic deformation. Calculate the resulting strain? (Modulus of elasticity of copper, $Y=42\times {10}^{9}N{m}^{-2}$)

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. A capacitor of capacitance $2\mu \text{F}$ can withstand a maximum voltage of $10\text{kV}$. Another capacitor of capacitance $5\mu \text{F}$ can withstand a maximum voltage of $7\text{kV}$. If the capacitors are connected in series, the combination can withstand a maximum voltage of

1. $10\text{kV}$
2. $6\text{kV}$
3. $14\text{kV}$
4. $4\text{kV}$

Q. Three capacitors of capacitance $3\mu \text{F},10\mu \text{F}$ and $15\mu \text{F}$ are connected in series to a battery of $100\text{V}$. The charge on $15\mu \text{F}$ is

1. $100\mu \text{C}$
2. $280\mu \text{C}$
3. $50\mu \text{C}$
4. $200\mu \text{C}$

Q. A parallel plate capacitor has two layers of dielectric as shown in figure. This capacitor is connected across a battery, then the ratio of potential difference across the dielectric layers is:

1. $\frac{4}{3}$
2. $\frac{1}{2}$
3. $\frac{1}{3}$
4. $\frac{3}{2}$

Q. An aluminium measuring tape which is correct at ${100}^{\circ }C$ measures the length of a line as 80 cm at ${50}^{\circ }$. If thermal coefficient of linear expansion of aluminium is of $2.50\times {10}^{-5}pe{r}^{\circ }C$ the correct length of the line is

1. 79.92 cm
2. 79.68 cm
3. 80.08cm
4. 80.32 cm