Question
In the given circuit, charge $${Q_2}$$ on the $$2\mu F$$ capacitor changes as $$C$$ is varied from $$1\mu F$$ to $$3\mu F.$$ $${Q_2}$$ as a function of $$'C'$$ is given properly by: (figures are drawn schematically and are not to scale)
In the given circuit, charge $${Q_2}$$ on the $$2\mu F$$ capacitor changes as $$C$$ is varied from $$1\mu F$$ to $$3\mu F.$$ $${Q_2}$$ as a function of $$'C'$$ is given properly by: (figures are drawn schematically and are not to scale)
A.
B.
C.
D.
Answer :
Solution :
From figure, $${Q_2} = \frac{2}{{2 + 1}}Q = \frac{2}{3}Q$$
$$\eqalign{ & Q = E\left( {\frac{{C \times 3}}{{C + 3}}} \right) \cr & \therefore {Q_2} = \frac{2}{3}\left( {\frac{{3CE}}{{C + 3}}} \right) = \frac{{2CE}}{{C + 3}} \cr} $$
Therefore graph D correctly dipicts.
From figure, $${Q_2} = \frac{2}{{2 + 1}}Q = \frac{2}{3}Q$$
$$\eqalign{ & Q = E\left( {\frac{{C \times 3}}{{C + 3}}} \right) \cr & \therefore {Q_2} = \frac{2}{3}\left( {\frac{{3CE}}{{C + 3}}} \right) = \frac{{2CE}}{{C + 3}} \cr} $$
Therefore graph D correctly dipicts.
