Question
Explain the series connection of capacitors.
✓
Answer
→As shown in fig. (a), two capacitors $C _1$ and $C _2$ are connected in series.
→The left plate of $C _1$ and the right plate of $C _2$ are connected to two terminals of a battery, and have charges $Q$ and $-Q$ on them, respectively.
→Consequently the right plate of $C _1$ has charge $-Q$ and left plate of $C_2$ has charge $Q$ induced on it.
→Like this, even though the capacitors may have different capacitance, the charge on them (the charge on each capacitor plate) is same.
→Suppose, the potential difference between two terminals of $C_1$ and $C_2$ is $V_1$ and $V_2$ respectively.
→The total potential drop V across the combination will be :
$\begin{aligned}
V & = V _1+ V _2 \\
\text { but } C _1 & =\frac{ Q }{ V _1} \\
\therefore V _1 & =\frac{ Q }{ C _1}
\end{aligned}$
Similarly we get $V_2=\frac{Q}{C_2}$
$\begin{array}{l}
\therefore \text { From eq }{ }^{ n } \text { (1) } \\
V =\frac{ Q }{ C _1}+\frac{ Q }{ C _2} \\
\therefore \quad \frac{ V }{ Q }=\frac{1}{ C _1}+\frac{1}{ C _2} \\
\end{array}$
→Suppose, the equivalent capacitance for the given combination of capacitors is C , then,
$\begin{array}{l}
\therefore C =\frac{ Q }{ V } \\
\therefore \quad \frac{1}{ C }=\frac{ V }{ Q }
\end{array}\$
$\therefore$ From equation (2) and (3)
$\therefore \frac{1}{ C }=\frac{1}{ C _1}+\frac{1}{ C _2}$
→As shown in fig. (b), n capacitors are connected in series.
→Their capacitance are $C _1, C _2, C _3$ $C _n$ respectively. Electric charge on each of those, is Q .
→Suppose the p.d. across these capacitors, are $V _1$, $V _2, V_3 \ldots . V _n$
→The total p.d. of the series combination will be :
$\begin{aligned}
V & = V _1+ V _2+ V _3+\ldots .+ V _n \\
\therefore V & =\frac{ Q }{ C _1}+\frac{ Q }{ C _2}+\frac{ Q }{ C _3}+\ldots .+\frac{ Q }{ C _n} \\
\therefore \frac{ V }{ Q } & =\frac{1}{ C _1}+\frac{1}{ C _2}+\frac{1}{ C _3}+\ldots .+\frac{1}{ C _n}
\end{aligned}$
→Suppose, the equivalent (/ effective) capacitance for the given series combination of capacitors is C .
$\begin{array}{l}
\therefore C =\frac{ Q }{ V } \\
\therefore \frac{1}{ C }=\frac{ V }{ Q }
\end{array}$
→From equations (4) and (5),
$\therefore \frac{1}{ C }=\frac{1}{ C _1}+\frac{1}{ C _2}+\frac{1}{ C _3}+\ldots .+\frac{1}{ C _n}$
→Suppose, the capacitance of each capacitor is same.
Then we get the equivalent capacitance.
$C _{\text {eq }}=\frac{ C }{n}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Define the term self-inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self-inductance L to build up a current I through it.
Derive the formula of electric field for a point on the axis of electric dipole.
Explain the de-Broglie wavelength by explaining the waveform of matter.
- State Bohr’s quantization condition for defining stationary orbits. How does de Broglie hypothesis explain the stationary orbits?
- Find the relation between the three wavelengths$\lambda_{1} , \lambda_{2}$ and$\lambda_{3}$ from the energy level diagram shown below.
A small piece of wood is floating on the surface of a 2.5m deep lake. Where does the shadow form on the bottom when the sun is just setting? Refractive index of water $=\frac{4}{3}.$
→Name the parts of the electromagnetic spectrum which is:
- Suitable for radar systems used in aircraft navigation.
- Used to treat muscular strain.
- Used as a diagnostic tool in medicine.
Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2eV collide with the atoms of the gas?
The band gap between the valence and the conduction bands in zinc oxide (ZnO) is 3.2eV. Suppose an electron in the conduction band combines with a hole in the valence band and the excess energy is released in the form of electromagnetic radiation. Find the maximum wavelength that can be emitted in this process.
When a charged comb is brought near a small piece of paper, it attracts the piece. Does the paper become charged when the comb is brought near it?
Write the definition of wavefront. Using Huygens' principle, draw the shape of a plane wave incident on a convex lens and the refracted wave body.
###
(a) When a wave propagates from a rarer medium to a denser medium, then which characteristic of that wave does not change and why?
(b) The refractive indices of two mediums are $\mu_1$ and $\mu_2$, what will be the ratio of velocities in the wave in them?
→###
(a) When a wave propagates from a rarer medium to a denser medium, then which characteristic of that wave does not change and why?
(b) The refractive indices of two mediums are $\mu_1$ and $\mu_2$, what will be the ratio of velocities in the wave in them?