MHT CET · Physics · Alternating Current
If the conductance and capacitance are both doubled in \(L-C\) - \(R\) circuit, the resonant frequency of the circuit will
- A decrease to one-half the original value
- B decrease to one-fourth the original value
- C increase to twice the original value
- D decrease to twice the original value
Answer & Solution
Correct Answer
(A) decrease to one-half the original value
Step-by-step Solution
Detailed explanation
The resonant frequency
\(
v_{0}=\frac{1}{2 \pi \sqrt{L C}} \Rightarrow v_{0} \propto \frac{1}{\sqrt{L C}}
\)
If conductance and capacitance both are doubled, then
\(
v_{0}=\frac{1}{2}\left(\frac{1}{2 \pi} \sqrt{L C}\right)
\)
So, the resonant frequency will decrease to one-half of the original value.
\(
v_{0}=\frac{1}{2 \pi \sqrt{L C}} \Rightarrow v_{0} \propto \frac{1}{\sqrt{L C}}
\)
If conductance and capacitance both are doubled, then
\(
v_{0}=\frac{1}{2}\left(\frac{1}{2 \pi} \sqrt{L C}\right)
\)
So, the resonant frequency will decrease to one-half of the original value.
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
- In biprism experiment, the \(4^{\text {th }}\) dark band is formed opposite to one of the slits. The wavelength of light used is
( \(\mathrm{D}=\) distance between source and screen, \(d\) = distance between the slits)MHT CET 2022 Easy - A photoelectric cell is illuminated by a point source of light \(1 \mathrm{~m}\) away. When the source is shifted to \(2 \mathrm{~m}\) thenMHT CET 2007 Medium
- \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are three parallel conductors of equal lengths carrying currents I, I and 2I respectively. Distance between A and \(B\) is ' \(x\) ' and that between B and \(C\) is also ' \(x\) '. \(F_1\) is the force exerted by conductor \(\mathrm{B}\) on \(\mathrm{A}\). \(\mathrm{F}_2\) is the force exerted by conductor \(\mathrm{C}\) on \(\mathrm{A}\). Current \(\mathrm{I}\) in \(\mathrm{A}\) and \(\mathrm{I}\) in \(\mathrm{B}\) are in same direction and current \(2 \mathrm{I}\) in \(\mathrm{C}\) is in opposite direction. ThenMHT CET 2021 Easy
- The coil of inductance \(0.25 \mathrm{mH}\) has a reactance of \(330 \Omega\), when connected to an a.c. source. The frequency of a.c. source is (Take \(\left.\pi=\frac{22}{7}\right)\)MHT CET 2022 Easy
- To use a transistor as an amplifierMHT CET 2011 Medium
- An electron is travelling along the \(x\) -direction. It encounters a magnetic field in the \(y\) -direction. Its subsequent motion will beMHT CET 2007 Hard
More PYQs from MHT CET
- If random variable thenMHT CET 2016 Medium
- Which of the following salt contain interstitial water molecule in it?MHT CET 2020 Easy
- Let k be a non-zero real number.
If \(\mathrm{f}(x)=\left\{\begin{array}{cc}\frac{\left(\mathrm{e}^x-1\right)^2}{\sin \left(\frac{x}{\mathrm{k}}\right) \log \left(1+\frac{x}{4}\right)} & , x \neq 0 \ 12 & , x=0\end{array}\right.\)
is a continuous function, then the value of \(k\) isMHT CET 2024 Hard - Let \(f: R \rightarrow R\) be a function such that \(\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \prime}(2)+6, x \in \mathrm{R}\), then \(\mathrm{f}(2)\) equalsMHT CET 2023 Easy
- What amount of oxygen is used at S.T.P to obtain \(9 \mathrm{~g}\) water from sufficient amount of hydrogen gas?MHT CET 2021 Medium
- For a substance, fraction of its initial quantify \(\left(\mathrm{N}_0\right)\) which will disintegrate in its average life time is about \((\mathrm{e}=2.71)\)MHT CET 2022 Medium