JEE Mains · Physics · STD 12 - 14. Semicondutor electronics
In series \(LCR\) circuit, the capacitance is changed from \(\mathrm{C}\) to \(4 \mathrm{C}\). To keep the resonance frequency unchanged, the new inductance should be _______.
- A reduced by \(\frac{1}{4} \mathrm{~L}\)
- B increased by \(2 \mathrm{~L}\)
- C reduced by \(\frac{3}{4} \mathrm{~L}\)
- D increased to \(4 \mathrm{~L}\)
Answer & Solution
Correct Answer
(C) reduced by \(\frac{3}{4} \mathrm{~L}\)
Step-by-step Solution
Detailed explanation
\(\omega^{\prime}=\omega\) \(\frac{1}{\sqrt{\mathrm{L}^{\prime} \mathrm{C}^{\prime}}}=\frac{1}{\sqrt{\mathrm{LC}}}\) \(\therefore \mathrm{L}^{\prime} \mathrm{C}^{\prime}=\mathrm{LC}\) \(\mathrm{L}^{\prime}(4 \mathrm{C})=\mathrm{LC}\) \(\mathrm{L}^{\prime}=\frac{\mathrm{L}}{4}\)…
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 proton and an electron have the same de Broglie wavelength. If \(K_p\) and \(K_e\) be the kinetic energies of proton and electron respectively. Then choose the correct relation :JEE Mains 2024 Hard
- A uniform cylindrical rod of length \(L\) and radius \(r\), is made from a material whose Young's modulus of Elasticity equals \(Y\). When this rod is heated by temperature \(T\) and simultaneously subjected to a net longitudinal compressional force \(F\), its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals toJEE Mains 2019 Hard
- Two blocks of masses \(m\) and \(M\) are connected by means of a metal wire of cross-sectional area \(A\) passing over a frictionless fixed pulley as shown in the figure. The system is then released. If \(M = 2\, m\), then the stress produced in the wire is
JEE Mains 2013 Hard - The energy released if hydrogen atoms are combined to form \(^{4}_{2}\text{He}\) is __________ MeV. (Take binding energies per nucleon of \(^{2}_{1}\text{H}\) and \(^{4}_{2}\text{He}\) as \(1.1\) MeV and \(7.2\) MeV, respectively)JEE Mains 2026 Medium
- A galvanometer with its coil resistance \(25\,\Omega \) requires a current of \(1\,mA\) for its full deflection. In order to construct an ammeter to read up to a current of \(2\,A,\) the approximate value of the shunt resistance should beJEE Mains 2018 Hard
- A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,JEE Mains 2025 Easy
More PYQs from JEE Mains
- The value of \(\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)\) is equal toJEE Mains 2022 Easy
- Let the position vectors of the vertices \(A, B\) and \(C\) of a tetrahedron \(A B C D\) be \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{k}\) and \(2 \hat{i}+\hat{j}-\hat{k}\) respectively. The altitude from the vertex \(D\) to the opposite face \(A B C\) meets the median line segment through \(A\) of the triangle \(A B C\) at the point \(E\). If the length of \(A D\) is \(\frac{\sqrt{110}}{3}\) and the volume of the tetrahedron is \(\frac{\sqrt{805}}{6 \sqrt{2}}\), then the position vector of \(E\) isJEE Mains 2025 Hard
- The equation of circle described on the chord \(3x + y+ 5\, = 0\) of the circle \(x^2 + y^2\, = 16\) as diameter isJEE Mains 2014 Hard
- If \(y = y ( x ), x \in\left(0, \frac{\pi}{2}\right)\) be the solution curve of the differential equation \(\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=\)\(2 e ^{-4 x }(2 \sin 2 x +\cos 2 x )\), with \(y \left(\frac{\pi}{4}\right)= e ^{-\pi}\), then \(y \left(\frac{\pi}{6}\right)\) is equal to.JEE Mains 2022 Hard
- A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is
JEE Mains 2014 Hard - A gas balloon is going up with a constant velocity of \(10\) m/s. When this balloon reached a height of \(75\) m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take \(g=10\) m/s\(^2\))JEE Mains 2026 Medium