Competishun Header
[jee_simple_nav]
JEE MAIN 2024
09-04-24 S1
Question
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is:
Select the correct option:
A
$\frac{11 \varepsilon_0 \mathrm{~A}}{18 \mathrm{~d}}$
B
$\frac{13 \varepsilon_0 \mathrm{~A}}{17 d}$
C
$\frac{11 \varepsilon_0 \mathrm{~A}}{20 \mathrm{~d}}$
D
$\frac{18 \varepsilon_0 \mathrm{~A}}{11 \mathrm{~d}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
All capacitor are in parallel combination. Also effective area is common area only $$ \begin{aligned} & \Rightarrow C_{e q}=C_1+C_2+C_3 \\ & \Rightarrow C_{e q}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)} \\ & \Rightarrow C_{e q}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right) \\ & \Rightarrow C_{e q}=\frac{11 A \varepsilon_0}{18 d} \end{aligned} $$
Question Tags
JEE Main
Physics
Medium
Start Preparing for JEE with Competishun
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE Advance 20082008
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...
JEE AdvanceChemistryEasy
View Solution
QJEE Advance 20082008
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...
JEE AdvanceChemistryEasy
View Solution
QJEE Advance 20082008
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...
JEE AdvanceChemistryEasy
View Solution
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The distance of the point...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The shortest distance between $\mathrm{L}_1$...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The unit vector perpendicular to...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
Suppose four distinct positive numbers $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \mathrm{a}_4$ are in G.P. Let $\mathrm{b}_1=\mathrm{a}_1, \mathrm{~b}_2=\mathrm{b}_1+\mathrm{a}_2, \mathrm{~b}_3=\mathrm{b}_2+ \mathrm{a}_3$ and $\mathrm{b}_4=\mathrm{b}_3+\mathrm{a}_4$. STATEMENT-1:...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
View Solution
QJEE ADVANCE 20112011
Match the statements given in Column I with the intervals/union of intervals given in Column II
JEE AdvanceMathematicsEasy
View Solution
QJEE ADVANCE 20112011
Match the statements given in Column I with the values given in Column II
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
Let a solution $y=y(x)$ of the differential equation $x \sqrt{x^2-1} d y-y \sqrt{y^2-1} d x=0$ satisfy $y(2)=\frac{2}{\sqrt{3}}$. STATEMENT-1 : $...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
View Solution
QJEE Advance 20082008
Consider $$ \begin{aligned} & L_1: 2 x+3 y+p-3=0 \\ & L_2: 2 x+3 y+p+3=0 \end{aligned} $$ where $p$ is a...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
View Solution
QJEE ADVANCE 20112011
Let M be a $3 \times 3$ matrix satisfying $$ \mathbf{M}\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{c} -1 \\ 2...
JEE AdvanceMathematicsEasy
View Solution
QJEE ADVANCE 20112011
Let $y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x), y(0)=0, x \in \mathbb{R}$, where $f^{\prime}(x)$ denotes $\frac{d f(x)}{d x}$ and $g(x)$ is a given nonconstant...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20082008
STATEMENT-1: $\quad \mathrm{Pb}^{4+}$ compounds are stronger oxidizing agents than $\mathrm{Sn}^{4+}$ compounds. and STATEMENT-2: The higher oxidation states for the group...
JEE AdvanceChemistryEasy
View Solution