MHT CET · Physics · Capacitance
If the equivalent capacitance between \(\mathrm{A}\) and \(\mathrm{B}\) of the combination of capacitors shown in figure is \(3 \mathrm{C}\), the capacitor \(\mathrm{C}^{\prime}\) 'is equal to
- A 5C
- B 4C
- C 7C
- D 6C
Answer & Solution
Correct Answer
(D) 6C
Step-by-step Solution
Detailed explanation
Consider figure below.
Equivalent capacitance between AP is:
\(\mathrm{C}_{\mathrm{AP}}=3(2 \mathrm{C})\)
As capacitors are connected parallel, the equivalent capacitance of AB is:
\(\frac{1}{\mathrm{C}_{\mathrm{AB}}}=\frac{1}{\mathrm{C}^{\prime}}+\frac{1}{6 \mathrm{C}}=\frac{6 \mathrm{C}+\mathrm{C}^{\prime}}{6 \mathrm{CC}^{\prime}}\)
We know \(\mathrm{C}_{\mathrm{AB}}=3 \mathrm{C}\),
\(\begin{aligned}
& \Rightarrow C_{A B}=\frac{6 C^{\prime}}{6 C+C^{\prime}}=3 C \\
& \Rightarrow 2 C^{\prime}=6 C+C^{\prime} \\
& \Rightarrow C^{\prime}=6 C
\end{aligned}\)
Equivalent capacitance between AP is:
\(\mathrm{C}_{\mathrm{AP}}=3(2 \mathrm{C})\)
As capacitors are connected parallel, the equivalent capacitance of AB is:
\(\frac{1}{\mathrm{C}_{\mathrm{AB}}}=\frac{1}{\mathrm{C}^{\prime}}+\frac{1}{6 \mathrm{C}}=\frac{6 \mathrm{C}+\mathrm{C}^{\prime}}{6 \mathrm{CC}^{\prime}}\)
We know \(\mathrm{C}_{\mathrm{AB}}=3 \mathrm{C}\),
\(\begin{aligned}
& \Rightarrow C_{A B}=\frac{6 C^{\prime}}{6 C+C^{\prime}}=3 C \\
& \Rightarrow 2 C^{\prime}=6 C+C^{\prime} \\
& \Rightarrow C^{\prime}=6 C
\end{aligned}\)
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 \(5 \mathrm{~m}\) long aluminium wire \(\left(Y=7 \times 10^{10} \mathrm{Nm}^{-2}\right.\) ) of diameter \(3 \mathrm{~mm}\) supports a \(40 \mathrm{~kg}\) mass. In order to have the same elongation in the copper wire \(\left(Y=12 \times 10^{10} \mathrm{Nm}^{-2}\right)\) of the same
length under the same weight, the diameter should now be (in \(\mathrm{mm}\) )MHT CET 2009 Hard - Acceleration of an electron in the first Bohr's orbit is proportional to \(\mathrm{m}=\) mass of electron, \(\mathrm{r}=\) radius of the orbit, \(\mathrm{h}=\) Planck's constant)MHT CET 2024 Medium
- A particle of mass \(m\) is rotating in a plane in circularpath of radius \(r\). Its angular momentum is \(L\). The centripetal force acting on the particle isMHT CET 2009 Medium
- If \(g\) is the acceleration due to gravity on earth's surface, the gain of the potential energy of an object of mass \(m\) raised from the surface of the earth to a height equal to the radius \(R\) of the earth isMHT CET 2008 Medium
- A ball rises to surface at a constant velocity in liquid whose density is 3 times greater than that of the material of the ball. The ratio of force of friction acting on the rising ball to its weight isMHT CET 2024 Hard
- Two parallel air capacitors have their plate areas \(100 \mathrm{~cm}^2\) and \(500 \mathrm{~cm}^2\), respectively. They have the same charge and potential. If the distance between the plates of the first capacitor is \(0.5 \mathrm{~mm}\), the distance between the plates of the second capacitor isMHT CET 2022 Easy
More PYQs from MHT CET
- If the Cartesian equation of a line is \(6 x-2=3 y+1=2 z-2\), then the vector equation of the line isMHT CET 2023 Easy
- Equation of the plane passing through the point \((2,0,5)\) and parallel to the vectors \(\hat{i}-\hat{j}+\hat{k}\) and \(3 \hat{i}+2 \hat{j}+\hat{k}\) isMHT CET 2021 Easy
- The vector equation of the line whose Cartesian equations are \(y=2\) and \(4 x-3 z+5=0\) isMHT CET 2021 Medium
- Match Assisted Reproductive Technologies in column I with their process in column II and select the correct option
Column I Column II a. ZIFT i. Single sperm cell is injected directly in cytoplasm of an ovum b. GIFT ii. Fertilized egg is transferred to fallopian tube for further development c. ICSI iii. Sperms are introduced into the Uterus d. IUI iv. Ova and sperms are directly injected into regions of the oviduct where fertilization occurs. MHT CET 2022 Easy - The force required to take away a flat circular plate of radius 2 \(\mathrm{cm}\) from the surface of water is \(\left[\right.\) Surface tension of water \(\left.=70 \times 10^{-3} \mathrm{Nm}^{-1}, \pi=\frac{22}{7}\right]\)MHT CET 2021 Medium
- Which from following complexes, the central metal ion does NOT obey EAN rule? (Atomic number - \(\mathrm{Pt}=78, \mathrm{Cu}=29, \mathrm{Zn}=30, \mathrm{Fe}=26\) )MHT CET 2020 Medium