Question

प्रश्न-10 तीन संधारित्र जिनकी धारिताएँ क्रमश: 4F, 6 UF तथा 12 uF हैं, श्रेणीक्रम में जोड़े
गए हैं, तो संयोजन की तुल्य धारिता ज्ञात कीजिए।​

Answer 1

SOLUTION

GIVEN

Three capacitors whose capacitances are 4 μF , 6 μF and 12 μF respectively, are added in series

TO DETERMINE

The equivalent capacitance of the combination.

EVALUATION

Here it is given that three capacitors whose capacitances are 4 μF , 6 μF and 12 μF respectively, are added in series

So by the given

$\sf{C_1 = 4 \: \mu F \: , \: C_2 = 6 \: \mu F \: , \: C_3 = 12 \: \mu F,}$

Let the equivalent capacitance of the combination = C

Thus we have

$\displaystyle\sf{ \frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} }$

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12} }$

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{3 + 2 + 1}{12} }$

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{6}{12} }$

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{1}{2} }$

$\displaystyle\sf{ \implies \: C = 2 }$

FINAL ANSWER

The equivalent capacitance of the combination = 2 μF

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