SATHEE: Electrostatics Question 592

Electrostatics Question 592

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 [KCET 1999]

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:

$C_{1} + C_{2} + C_{3} = 12$ ….(i)

$C_{1} C_{2} C_{3} = 48$ ….(ii)

$C_{1} + C_{2} = 6$ ….(iii)

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

From equation (ii) and (iv) $C_{1} C_{2} = 8$

Also ${(C_{1} - C_{2})}^{2} = {(C_{1} + C_{2})}^{2} - 4 C_{1} C_{2}$

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

therefore $C_{1} C_{2} = 2$ …..(v)

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

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Electrostatics Question 592

Question: The equivalent capacitance of three capacitors of capacitance C1,C2 and C3 are connected in parallel is 12 units and product C1.C2.C3=48 . When the capacitors C1 and C2 are connected in parallel, the equivalent capacitance is 6 units. Then the capacitance are [KCET 1999]

Options:

Answer:

Solution:

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