The eftective capacitances of two capacitors are 3 μF and 16 μF, when they are connected in seri

Name: Problem 1611, Chapter 11: JEE Physics
Uploaded: 2021-10-02T14:37:28-08:00
Duration: 1 min 17 s
Channel: Narayan Hari
Description: The eftective capacitances of two capacitors are 3 μF and 16 μF, when they are connected in series and parallel respectively. The capacitance of each capacitor is (A) 2 μF, 14 μF (B) 4 μF, 12 μF (C) 6 μF, 8 μF (D) 10 μF, 6 μF

step 1 As we know that when capacitor is in series, the value between C1, C2 can be given by C1C2 by C1

The eftective capacitances of two capacitors are 3 μF and 16...

The eftective capacitances of two capacitors are $3 \mu \mathrm{F}$ and $16 \mu \mathrm{F}$, when they are connected in series and parallel respectively. The capacitance of each capacitor is (A) $2 \mu \mathrm{F}, 14 \mu \mathrm{F}$ (B) $4 \mu \mathrm{F}, 12 \mu \mathrm{F}$ (C) $6 \mu \mathrm{F}, 8 \mu \mathrm{F}$ (D) $10 \mu \mathrm{F}, 6 \mu \mathrm{F}$

The eftective capacitances of two capacitors are $3 \mu \mathrm{F}$ and $16 \mu \mathrm{F}$, when they are connected in series and parallel respectively. The capacitance of each capacitor is
(A) $2 \mu \mathrm{F}, 14 \mu \mathrm{F}$
(B) $4 \mu \mathrm{F}, 12 \mu \mathrm{F}$
(C) $6 \mu \mathrm{F}, 8 \mu \mathrm{F}$
(D) $10 \mu \mathrm{F}, 6 \mu \mathrm{F}$

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Key Concepts

Parallel Connection of Capacitors

For capacitors connected in parallel, the equivalent capacitance is simply the sum of the individual capacitances. This configuration means that all the capacitors experience the same voltage, and the overall storage capacity is the aggregate of each capacitor’s capacity.

Setting Up and Solving Simultaneous Equations

When provided with effective capacitances from series and parallel combinations, the problem requires forming simultaneous equations based on the series and parallel formulas. Solving these equations allows one to determine the individual capacitance values, which is a common technique in circuit analysis.

Series Connection of Capacitors

In a series arrangement, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances. This concept is fundamental in circuits where capacitors are arranged end-to-end, affecting how the overall charge and voltage distribute across the components.

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