MHT CET · Physics · Alternating Current
The frequency for which a \(5 \mu \mathrm{F}\) capacitor has a reactance of \(\frac{1}{1000} \Omega\) is given by
- A \(\frac{1}{1000} \mathrm{~Hz}\)
- B \(1000 \mathrm{~Hz}\)
- C \(\frac{100}{\pi} \mathrm{MHz}\)
- D \(\frac{1000}{\pi} \mathrm{Hz}\)
Answer & Solution
Correct Answer
(C) \(\frac{100}{\pi} \mathrm{MHz}\)
Step-by-step Solution
Detailed explanation
Concept: reactance of capacitor is
\(X_c=\frac{1}{\omega c}=\frac{1}{2 \pi f C}\)
Given \(X_c=10^{-3} \Omega, C=5 \times 10^{-6} \mathrm{~F}\)
\(\begin{aligned}
& \therefore 10^{-3} \Omega=\frac{1}{2 \pi \mathrm{f}\left(5 \times 10^{-6}\right)} \\
& \Rightarrow \mathrm{f}=\frac{1}{10 \pi \times 10^{-9}} \mathrm{~Hz}=\frac{10^8}{\pi} \mathrm{Hz}=\frac{100}{\pi} \mathrm{MHz}
\end{aligned}\)
\(X_c=\frac{1}{\omega c}=\frac{1}{2 \pi f C}\)
Given \(X_c=10^{-3} \Omega, C=5 \times 10^{-6} \mathrm{~F}\)
\(\begin{aligned}
& \therefore 10^{-3} \Omega=\frac{1}{2 \pi \mathrm{f}\left(5 \times 10^{-6}\right)} \\
& \Rightarrow \mathrm{f}=\frac{1}{10 \pi \times 10^{-9}} \mathrm{~Hz}=\frac{10^8}{\pi} \mathrm{Hz}=\frac{100}{\pi} \mathrm{MHz}
\end{aligned}\)
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
- With an increase in temperature, surface tension of liquid (except molten copper and cadmium)MHT CET 2010 Medium
- A particle is revolving in anticlockwise sense along the circumference of a circle of radius 'r' with linear velocity 'v', then the angle between ' \(\mathrm{v}^{\prime}\) and angular velocity '\(\omega^{\prime}\) will beMHT CET 2020 Easy
- A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant ' \(\mathrm{K}\) ' is inserted between the plates and then taken out. Then electric field between the platesMHT CET 2023 Easy
- A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled and the current is made \(\left(\frac{1}{4}\right)^{\mathrm{th}}\) then the new value of magnetic field will beMHT CET 2024 Easy
- Two loops ' \(A\) ' and ' \(B\) ' of radii ' \(R_1\) ' and ' \(R_2\) ' are made from uniform wire. If moment of inertia of ' \(A\) ' is ' \(I_A\) ' and that ' \(B\) ' is ' \(\mathrm{B}_{\mathrm{B}}\) ', then \(R_2 / R_1\) is \(\left[\frac{I_A}{I_B}=27\right]\)MHT CET 2024 Medium
- Two satellites of masses 'm' and '2m' are revolving in a circular orbit of radius 'r',
around the earth. The ratio of their frequencies of revolution will beMHT CET 2020 Medium
More PYQs from MHT CET
- Which of the following organic compounds could not be dried by anhydrous \(\mathrm{CaCl}_{2}\) ?MHT CET 2012 Hard
- The function \(\mathrm{f}(x)=x^3-6 x^2+9 x+2\) has maximum value when \(x\) isMHT CET 2023 Easy
- What is the conductivity of 0.02 M AgNO 3 solution having cell constant \(1.1 \mathrm{~cm}^{-1}\) and resistance is 94.5 ohms?MHT CET 2024 Medium
- An electron accelerated through potential difference ' \(V\) ' passes through a uniform
transverse magnetic field and experiences a force ' \(\mathrm{F}^{\prime}\). If the accelerating potential
is increased to '2V', the electron in the same magnetic field will experience a forceMHT CET 2020 Medium - If \(A\left[\begin{array}{lll}3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6\end{array}\right]\) and \(\mathrm{A}_{\mathrm{ij}}\) are cofactors of the elements \(\mathrm{a}_{\mathrm{ij}}\) of \(\mathrm{A}\), then \(a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}\) is equal toMHT CET 2021 Medium
- Identify the correct molecular formula of 'Oleum' from following.MHT CET 2025 Easy