Physics NCERT Exemplar Solutions Class 12th Chapter Ten Physics NCERT Exemplar Solutions Class 12th Chapter Six Class 12th Physics Mechanical Properties of Fluids

Two capacitors having C₁ and C₂ respectively are connected as shown in figure. Initially, capacitor C₁ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C₁ is not connected to uncharged capacitor C₂ by closing the switch S. The amount of charge on the capacitor C₂, after equilibrium, is

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>V</mi> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mi>V</mi> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>V</mi> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>V</mi> </mrow> </math> </span></p>

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Payal Gupta | Contributor-Level 10

6 months ago

Correct Option - 1

Detailed Solution:

After switch 'S' is closed

$Q_{1} + Q_{2} = C_{1} V$ - (1)

Using KVL

$\frac{Q_{1}}{C_{1}} - \frac{Q_{2}}{C_{2}} = 0$

$Q_{1} = Q_{2} \frac{C_{1}}{C_{2}}$ - (2)

from (1) & (2)

$\Rightarrow Q_{2} [\frac{C_{1} + C_{2}}{C_{2}}] = C_{1} V \Rightarrow Q_{2} = (\frac{C_{1} C_{2}}{C_{1} + C_{2}}) V$

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Similar Questions for you

A water drop of radius $1 μ m$ falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10^-⁵ Nsm^-² and its density is negligible as compared to that of water 10⁶ gm^-³. Terminal velocity of the water drop is:

(Take acceleration due to gravity = 10 ms^-²)

Alok Kumar Singh

NLM 1

$ρ_{ω} \frac{4}{3} π r^{3} g = 6 π η r V_{T}$

$\frac{ρ_{ω} 4}{3} π r^{2} g =$ $6 π η v_{T}$

$V_{T} = \frac{4}{3} \frac{ρ_{ω} π r^{2} g}{6 π η}$

$= \frac{2}{9} \times 1 0^{3} \times \frac{{(1 0^{- 6})}^{2} \times 10}{1.8 \times 1 0^{- 5}}$

$= 0.1234 \times 1 0^{- 3}$

vT = 123.4 × 10^-6m/sec

If p is the density and $η$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is:

Kindly consider the following answer

$R e = \frac{ρ v d}{η}$

A water drop of radius 1cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be:

(Given π = 3.14)

$\frac{4}{3} π R^{3} = 729 \frac{4}{3} π r^{3}$

R³ = 729r³

$R = (729) \frac{1}{3} (r) (\frac{1}{3})$

R = 9r

$Δ u = T (4 π r^{2}) \times 729 - T \times 4 π R^{2}$

$= T \times 4 π \times 8 R^{2}$

$\begin{array}{l} = 75.39 \times 1 0^{- 5} J \\ Δ u = 7.5 \times 1 0^{- 4} J \end{array}$

Consider a cylindrical tank of radius 1m is filled with water. The top surface of water is at 15m front the bottom of the cylinder. There is a hole on the wall of a cylinder at a height of 5m from the bottom. A force of 5 × 10⁵N is applied an the top surface of water using a piston. The speed of ifflux from the hole will be:

(given atmospheric pressure P_A = 1.01 × 10⁵Pa, density of water $ρ_{w} = 1000 k g / m^{3}$  and gravitational acceleration g = 10m/s²)

$ρ_{ω} = 1000 k g / m^{3}$

G = 10 m/s²

Using bernaulli’s eqn

$\frac{5 \times 1 0^{5}}{π} + ρ g \times 10 = ρ_{0} + \frac{1}{2} ρ V_{e}^{2}$

$= \sqrt[]{318} ? 17.8 m / s$

A pressure-pump has a horizontal tube of cross sectional area 10cm2 for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is:

[given : density of water = 1000 kg/m³]

A = 10 cm², V = 20 m/s

$F = \frac{d p}{d t} = ρ A V^{2} = 1 0^{3} \times 10 \times 1 0^{- 4} \times 400$

= 400 N.

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Physics NCERT Exemplar Solutions Class 12th Chapter Ten 2025

Physics NCERT Exemplar Solutions Class 12th Chapter Ten 2025

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