SATHEE: Electrostatics 5 Question 20

Electrostatics 5 Question 20

22. In the given circuit, charge $Q_{2}$ on the $2 μ F$ capacitor changes as $C$ is varied from $1 μ F$ to $3 μ F . Q_{2}$ as a function of $C$ is given properly by (figures are drawn schematically and are not to scale)

(2015 Main)

(a)

(b)

(c)

(d)

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Answer:

Correct Answer: 22. (a)

Solution:

Resultant of $1 μ F$ and $2 μ F$ is $3 μ F$ . Now in series, potential difference distributes in inverse ratio of capacity.

$∴ \frac{V_{3 μ F}}{V_{c}} = \frac{c}{3}$ or $V_{3 μ F} = \frac{c}{c + 3} E$

This is also the potential difference across $2 μ F$ .

$\begin{array}{ll} ∴ & Q_{2} = (2 μ F) (V_{2 μ F}) \\ or & Q_{2} = \frac{2 c E}{c + 3} = \frac{2}{1 + \frac{3}{c}} E \end{array}$

From this expression of $Q_{2}$ , we can see that $Q_{2}$ will increase with increase in the value of $c$ (but not linearly). Therefore, only options (a) and (b) may be correct.

Further, $\frac{d}{d c} (Q_{2}) = 2 E \frac{(c + 3) - c}{(c + 3)^{2}} = \frac{6 E}{(c + 3)^{2}}$

$=$ Slope of $Q_{2}$ verus $c$ graph

i.e. slope of $Q_{2}$ versus $c$ graph decreases with increase in the value of $c$ . Hence, the correct graph is (a).

Electrostatics 5 Question 20

22. In the given circuit, charge $Q_{2}$ on the $2 μ F$ capacitor changes as $C$ is varied from $1 μ F$ to $3 μ F . Q_{2}$ as a function of $C$ is given properly by (figures are drawn schematically and are not to scale)

Answer:

Solution:

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Electrostatics 5 Question 20

22. In the given circuit, charge Q2 on the 2μF capacitor changes as C is varied from 1μF to 3μF.Q2 as a function of C is given properly by (figures are drawn schematically and are not to scale)

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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22. In the given circuit, charge $Q_{2}$ on the $2 μ F$ capacitor changes as $C$ is varied from $1 μ F$ to $3 μ F . Q_{2}$ as a function of $C$ is given properly by (figures are drawn schematically and are not to scale)