Figure shows charge ( q ) versus voltage ( V ) graph for series and...

Figure shows charge

( q )

versus voltage

( V )

graph for series and parallel combination of two given capacitors. The capacitances are:
Figure shows charge ( q ) versus voltage ( V ) graph for series and parallel combination of two given capacitors. The

Figure shows charge ( q ) versus voltage ( V ) graph for series and parallel combination of two given capacitors. The

Options

A $60\muF$ and $40\muF$
B $50\muF$ and $30\muF$
C $20\muF$ and $30\muF$
D $40\muF$ and $10\muF$

Correct answer

D. $40\muF$ and $10\muF$

Step-by-step solution

Q = CV

The slope of graph will give the equivalent capacitance of the combination.
From graph

A:

{C}_{1} + {C}_{2} = \dfrac{500}{10} = 50

…(i)
From graph

B:

\dfrac{{C}_{1}{C}_{2}}{{C}_{1} + {C}_{2}} = \dfrac{80}{10} = 8

…(ii)
From equation (i) & (ii)

{C}_{1}{C}_{2} = 400

…(iii)

{C}_{1} + \dfrac{400}{{C}_{1}} = 50

⇒ {C}_{1}^{2} - 50{C}_{1} + 400 = 0

{C}_{1} = \dfrac{50 \pm \sqrt{2500 - 1600}}{2} = \dfrac{50 \pm 30}{2}

= 10\muF, 40\muF

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