SATHEE: Electrostatics Question 647

Electrostatics Question 647

Question: The equivalent capacitance of three capacitors of Capacitance $C_{1} : C_{2}$ and $C_{3}$ are connected in parallel is 12 units and product $C_{1} . C_{2} . C_{3} = 48$ . When the capacitors $C_{1}$ and $C_{2}$ are connected in parallel, the equivalent capacitance is 6 units. Then the capacitance are

Options:

A) 2, 3, 7

B) 1.5, 2.5, 8

C) 1, 5, 6

D) 4, 2, 6

Show Answer

Answer:

Correct Answer: D

Solution:

[d] $C_{1} + C_{2} + C_{3} = 12$ … (i) $C_{1} C_{2} C_{3} = 48$ … (ii) $C_{1} + C_{2} = 6$ … (iii)

From equations (i) and (iii) $C_{3} = 6$ … (iv)

From equations (ii) and (iv) $C_{1} C_{2} = 8$ Also ${(C_{1} - C_{2})}^{2} = {(C_{1} + C_{2})}^{2} - 4 C_{1} C_{2}$

${(C_{1} - C_{2})}^{2} = {(6)}^{2} - 4 \times 8 = 4$

$\Rightarrow C_{1} - C_{2} = 2$ … (v)

On solving (iii) and (v) $C_{1} = 4$ , $C_{2} = 2$

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Electrostatics Question 647

Question: The equivalent capacitance of three capacitors of Capacitance C1:C2 and C3 are connected in parallel is 12 units and productC1.C2.C3=48 . When the capacitors C1 and C2 are connected in parallel, the equivalent capacitance is 6 units. Then the capacitance are

Options:

Answer:

Solution:

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