Electrostatics Physics - Electrostatics

An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as in adjoining figure. Then the equivalent capacitance between $A$ and  $B$ is

• A
  $1 \mu F$
• ✓
  $2 \mu F$
• C
  $\frac12 \mu F$
• D
  $\infty $

Answer: B.

Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistance $R_1, R_2$ and $R_3.$ Their charges, as a function of time shown in the graph below. The smallest of the three resistance is

• A
  $R_3$
• B
  $R_2$
• ✓
  $R_1$
• D
  Cannot be predicted

Answer: C.

• ✓
  
• B
  
• C
  
• D
  

Answer: A.

• A
  
• B
  
• ✓
  
• D
  

Answer: C.

$q_1, q_2, q_3$ and $q_4$ are point charges located at points as shown in the figure and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to the Gauss’s law

• A
  $\oint_s\left(\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}\right) \cdot d \vec{A}=\frac{q_1+q_2+q_s}{2 \varepsilon_0}$
• ✓
  $\oint_s\left(\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}\right) \cdot d \vec{A}=\frac{q_1+q_2+q_s}{\varepsilon_0}$
• C
  $\oint_s\left(\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}\right) \cdot d \vec{A}=\frac{\left(q_1+q_2+q_3+q_4\right)}{\varepsilon_0}$
• D
  None of the above

Answer: B.