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Question:

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: (figure are drawn schematically and are not to scale)

Solution:

Let the charge on the capacitor C be Q.
Charge on the combination of 1 and 2μF is also Q.
Q2 = 2/(1+2)Q = 2/3Q
But, Q = E(3C/(3+C))
∴Q2 = (2/3)E(3C/(3+C)) = 2EC/(3+C)
As we can see, since C is between 1 and 3, Q2 will increase until C=3.
Options (A) and (D) are eliminated.
slope of curve, dQ2/dC = (3+C)2E - EC(1)/(3+C)2 = 6E/(3+C)2
Thus, slope decreases as C increases.
Hence, (B) is the correct option.