Question:
Two circular plates each of radius '\(r\)' are kept parallel to each other distance '\(d\)' apart. The capacitance of the capacitor formed is '\(C_1\)'. If the radius of each of the plates is increased to \(\sqrt{3}\) times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes '\(C_2\)'. The ratio \(C_1:C_2\) is
Two circular plates each of radius '\(r\)' are kept parallel to each other distance '\(d\)' apart. The capacitance of the capacitor formed is '\(C_1\)'. If the radius of each of the plates is increased to \(\sqrt{3}\) times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes '\(C_2\)'. The ratio \(C_1:C_2\) is
Show Hint
Capacitance is proportional to area and inversely proportional to separation.
Updated On: Oct 1, 2026
- \(1:2\)
- \(1:4\)
- \(1:6\)
- \(6:1\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
For a parallel plate capacitor, \(C = \frac{\varepsilon_0 A}{d}\). For circular plates, \(A = \pi r^2\).
Step 2: Key Formula or Approach:
New radius \(= \sqrt3\,r\), so the new area is \(\pi\cdot 3r^2 = 3A\). New separation \(= \frac d2\).
Step 3: Detailed Explanation:
\[ C_2 = \frac{\varepsilon_0 (3A)}{d/2} = 6\cdot\frac{\varepsilon_0 A}{d} = 6C_1 \]
So \(\frac{C_1}{C_2} = \frac16\), which is \(1 : 6\).
Option D, \(6:1\), is the inverse ratio.
Final Answer:
\(C_1 : C_2 = 1 : 6\), option (C). \[ \boxed{1:6} \]
For a parallel plate capacitor, \(C = \frac{\varepsilon_0 A}{d}\). For circular plates, \(A = \pi r^2\).
Step 2: Key Formula or Approach:
New radius \(= \sqrt3\,r\), so the new area is \(\pi\cdot 3r^2 = 3A\). New separation \(= \frac d2\).
Step 3: Detailed Explanation:
\[ C_2 = \frac{\varepsilon_0 (3A)}{d/2} = 6\cdot\frac{\varepsilon_0 A}{d} = 6C_1 \]
So \(\frac{C_1}{C_2} = \frac16\), which is \(1 : 6\).
Option D, \(6:1\), is the inverse ratio.
Final Answer:
\(C_1 : C_2 = 1 : 6\), option (C). \[ \boxed{1:6} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Capacitance Questions
- A capacitor of unknown capacitance is connected across a battery of $V$ volt. The charge stored in it is $Q$ coulomb. When potential across the capacitor is reduced by $V'$ volt, the charge stored in it becomes $Q'$ coulomb. The potential $V$ is
- Light of wavelength \(\lambda\) strikes a photoelectric surface and electrons are ejected with energy \(E\). If the wavelength is changed to \(\lambda'\), the energy becomes twice the original value. Which one of the following relations is true for \(\lambda\) and \(\lambda'\)?
- In between the plates of parallel plate capacitor of plate separation '$d$' a dielectric plate of thickness '$t$' is inserted. The capacitance becomes one-third of the original capacity without dielectric. The dielectric constant of the plate is
- In between the plates of parallel plate capacitor of plate separation '$d$' a dielectric plate of thickness '$t$' is inserted. The capacitance becomes one-third of the original capacity without dielectric. The dielectric constant of the plate is
- The graph shows the variation of voltage (v) across the plates of two parallel plate capacitors $A$ and $B$ versus increase of charge $Q$ stored in them. Then
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions