Question

तीन संधारित्र जिनकी धारिताएँ क्रमश: 2pF, 3pF व 4 pF हैं, श्रेणीक्रम में जोड़े गए
हैं, तो संयोजन की तुल्य धारिता ज्ञात कीजिए।​

Answer 1

SOLUTION

GIVEN

Three capacitors whose capacitances are 2 μF , 3 μF and 4 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 2 μF , 3 μF and 4 μF respectively, are added in series

So by the given

$\sf{C_1 = 2 \: \mu F \: , \: C_2 = 3 \: \mu F \: , \: C_3 = 4 \: \mu F}$

Let the equivalent capacitance of the combination = C

Thus we have

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

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} }$

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{6 + 4 + 3}{12}}$

$\displaystyle\sf{ \implies \: \frac{1}{C} = \frac{13}{12}}$

$\displaystyle\sf{ \implies \: C= \frac{12}{13}}$

FINAL ANSWER

The equivalent capacitance of the combination

$\displaystyle\sf{ = \frac{12}{13} \: \mu F}$

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