MHT CET · Physics · Capacitance
Two circular metal plates each of radius ' \(r\) ' are kept parallel to each other distance 'd' apart. The capacitance of the capacitor formed is ' \(\mathrm{C}_1\) '. If the radius of each of the plates is increased to \(\sqrt{2}\) times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ' \(\mathrm{C}_2\) '. The ratio of the capacitances \(\mathrm{C}_1: \mathrm{C}_2\). is
- A \(1: 1\)
- B \(1: 2\)
- C \(1: 4\)
- D \(4: 1\)
Answer & Solution
Correct Answer
(C) \(1: 4\)
Step-by-step Solution
Detailed explanation
For the \(1^{\text {st }}\) capacitor,
\(\mathrm{C}_1=\frac{\varepsilon_0 \mathrm{~A}_1}{\mathrm{~d}}=\frac{\varepsilon_0 \pi \mathrm{r}^2}{\mathrm{~d}}\)
For the \(2^{\text {nd }}\) capacitor,
\(\begin{aligned}
& \mathrm{C}_2=\frac{\varepsilon_0 \mathrm{~A}_2}{\mathrm{~d}}=\frac{\varepsilon_0 \pi 2 \mathrm{r}^2}{\frac{d}{2}}=\frac{\varepsilon_0 4 \pi \mathrm{r}^2}{\mathrm{~d}}=4 \mathrm{C}_1 \\
\therefore \quad & \frac{\mathrm{C}_1}{\mathrm{C}_2}=\frac{\mathrm{C}_1}{4 \mathrm{C}_1}=\frac{1}{4}
\end{aligned}\)
\(\mathrm{C}_1=\frac{\varepsilon_0 \mathrm{~A}_1}{\mathrm{~d}}=\frac{\varepsilon_0 \pi \mathrm{r}^2}{\mathrm{~d}}\)
For the \(2^{\text {nd }}\) capacitor,
\(\begin{aligned}
& \mathrm{C}_2=\frac{\varepsilon_0 \mathrm{~A}_2}{\mathrm{~d}}=\frac{\varepsilon_0 \pi 2 \mathrm{r}^2}{\frac{d}{2}}=\frac{\varepsilon_0 4 \pi \mathrm{r}^2}{\mathrm{~d}}=4 \mathrm{C}_1 \\
\therefore \quad & \frac{\mathrm{C}_1}{\mathrm{C}_2}=\frac{\mathrm{C}_1}{4 \mathrm{C}_1}=\frac{1}{4}
\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A body is projected vertically, upwards from earth's surface with velocity \(2 V_e\) where \(V_e\) is the escape velocity from earth's surface. The velocity when body escapes the gravitational pull isMHT CET 2022 Hard
- Which of the following while in motion cannot be deflected by magnetic field?MHT CET 2008 Easy
- A diffraction pattern is obtained by making blue light incident on a narrow slit. If blue light is replaced by red light thenMHT CET 2022 Easy
- In case of rotational dynamics, which one of the following statements is correct?
\([\vec{\omega}=\) angular velocity, \(\vec{v}=\) linear velocity
\(\overrightarrow{\mathrm{r}}=\) radius vector, \(\vec{\alpha}=\) angular acceleration
\(\overrightarrow{\mathrm{a}}=\) linear acceleration, \(\overrightarrow{\mathrm{L}}=\) angular momentum
\(\overrightarrow{\mathrm{p}}=\) linear momentum, \(\vec{\tau}=\) torque,
\(\overrightarrow{\mathrm{f}}=\) centripetal force \(]\)MHT CET 2024 Medium - Two coils have a mutual inductance \(5 \times 10^{-3} \mathrm{H}\). The current changes in the first coil according to the equation \(\mathrm{I}_1=\mathrm{I}_0 \sin \omega \mathrm{t}\) where \(\mathrm{I}_0=10 \mathrm{~A}\) and \(\omega=100 \pi \mathrm{rad} / \mathrm{s}\). What is the value of the maximum e.m.f. in the coil?MHT CET 2024 Medium
- The electric potential at a point on the axis of an electric dipole is proportional to \([\mathrm{r}=\) distance between centre of the electric dipole and the point]MHT CET 2024 Easy
More PYQs from MHT CET
- Calculate the concentration of \(\mathrm{H}^{+}\)ions in a solution if \(\mathrm{pOH}\) is 11 .MHT CET 2023 Medium
- Cost function \(\mathrm{Z}\) given by \(\mathrm{Z}=4 \mathrm{x}+6 \mathrm{y}\) is to be minimized. The fessible region for this function \(\mathrm{Z}\) is the shaded region represented in the following figure. Then the minimum value of \(\mathrm{Z}\) is and occurs at the point
MHT CET 2022 Easy - \(16 \mathrm{~g}\) of oxygen gas expands isothermally and reversibly at \(300 \mathrm{~K}\) from \(10 \mathrm{dm}^{3}\) to \(100 \mathrm{dm}^{3}\). The work done is (in \(J\) )MHT CET 2009 Medium
- Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference between the beams is \(\pi / 2\) at point \(P\) and \(\pi\) at point \(Q\) on the screen. The difference between the resultant intensities at points \(P\) and \(Q\) is \(\left(\cos 90^{\circ}=0, \cos \pi=-1\right)\)MHT CET 2025 Medium
- The length of a potentiometer wire is \(L\). A cell of e.m.f. \(E\) is balanced at a length \(\frac{L}{3}\) from the positive end of the wire. If the length of the wire is increased \(\frac{L}{2}\) at what distance will the same cell gives a balance point?MHT CET 2022 Medium
- Instantaneous rate of a reaction is \(-\frac{1}{2} \frac{\mathrm{d}[\mathrm{x}]}{\mathrm{dt}}=-\frac{\mathrm{d}[\mathrm{y}]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{d}[\mathrm{z}]}{\mathrm{dt}}\), identify the reaction.MHT CET 2021 Easy