KCET · Physics · Alternating Current
The minimum value of effective capacitance that can be obtained by combining \( 3 \) capacitors of capacitances \( 1 \mathrm{pF}, 2 \mathrm{pF} \) and \( 4 \mathrm{pF} \) is
- A \( \frac{4}{7} \mathrm{pF} \)
- B \( 1 \mathrm{pF} \)
- C \( \frac{7}{4} \mathrm{pF} \)
- D \( 2 \mathrm{pF} \)
Answer & Solution
Correct Answer
(A) \( \frac{4}{7} \mathrm{pF} \)
Step-by-step Solution
Detailed explanation
The effective capacitance will be minimum when the threecapacitors are connected in series. The effective capacitance is given by
\(C_{1}=1 \mathrm{pF} \)
\(C_{2}=2 \mathrm{pF} C_{3}=4 \mathrm{pF} \)
\(\frac{1}{C_{e f f}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} \)
\(=\frac{1}{1 p F}+\frac{1}{2 p F}+\frac{1}{4 p F}=\frac{(4+2+1)}{4 p F}=\frac{7}{4} \)
Therefore \(\text C_{\text {eff }}=\frac{4}{7} p F\)
\(C_{1}=1 \mathrm{pF} \)
\(C_{2}=2 \mathrm{pF} C_{3}=4 \mathrm{pF} \)
\(\frac{1}{C_{e f f}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} \)
\(=\frac{1}{1 p F}+\frac{1}{2 p F}+\frac{1}{4 p F}=\frac{(4+2+1)}{4 p F}=\frac{7}{4} \)
Therefore \(\text C_{\text {eff }}=\frac{4}{7} p F\)
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
- Rutherford's atomic model could account forKCET 2011 Easy
- The output of a step down transformer is measured to be \( 48 \mathrm{~V} \) when connected to a \( 12 \mathrm{~W} \)
bulb. The value of peak current isKCET 2017 Easy - An electric dipole is kept in non-uniform electric field. It generally experiencesKCET 2019 Easy
- The resistivity of a semiconductor at room temperature is in betweenKCET 2022 Easy
- A vessel of height \(2 d\) is half-filled with a liquid of refractive index \(\sqrt{2}\) and the other half with a liquid of refractive index \(n\) (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will beKCET 2007 Hard
- A straight wire of length \( 50 \mathrm{~cm} \) carrying a current of \( 2.5 \mathrm{~A} \) is suspended in mid-air by a uniform magnetic field of \( 0.5 \mathrm{~T} \) (as shown in figure). The mass of the wire is \( \left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right) \)KCET 2017 Hard
More PYQs from KCET
- \( \int_{0}^{\pi / 4} \log \left(\frac{\sin x+\cos x}{\cos x}\right) d x \)KCET 2015 Medium
- The value of \( k \) such that the line \( \frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2} \) lies on the plane \( 2 x-4 y+z=7 \) isKCET 2018 Easy
- Net primary productivity (NPP) in an ecosystem isKCET 2019 Hard
- Two particles \(A\) and \(B\) are in motion. If the wavelength associated with particle \(A\) is \(5 \times 10^{-8} \mathrm{~m}\). Calculated the wavelength (in Ã…) associated with particle B if its momentum is half of \(\mathrm{A}\).KCET 2019 Easy
- A \( 100 \mathrm{~W} \) bulb is connected to an \( \mathrm{AC} \) source of \( 220 \mathrm{~V}, 50 \mathrm{~Hz} \). Then the current flowing through the bulb isKCET 2018 Easy
- A tiny spherical oil drop carrying a net charge \(q\) is balanced in still air, with a vertical uniform electric field of strèngth \(\frac{81}{7} \pi \times 10^5 \mathrm{~V} / \mathrm{m}\). When the field is switched OFF, the drop is observed to fall with terminal velocity \(2 \times 10^{-3} \mathrm{~ms}^{-1}\). Here \(g=9.8 \mathrm{~m} / \mathrm{s}^2\), viscosity of air is \(1.8 \times 10^{-5} \mathrm{Ns} / \mathrm{m}^2\) and density of oil is \(900 \mathrm{~kg}\) \(\mathrm{m}^{-3}\). The magnitude of \(q\) isKCET 2022 Hard