What Is a Capacitor
Following NCERT Section 2.11, a capacitor is a system of two conductors separated by an insulator. The two conductors carry charges $Q_1$ and $Q_2$ and sit at potentials $V_1$ and $V_2$. In practice they are given equal and opposite charges, $+Q$ on one and $-Q$ on the other, with a potential difference $V = V_1 - V_2$ between them. We restrict our study to this configuration.
Note the careful wording: $Q$ is called the charge of the capacitor, but it is actually the charge on only one conductor. The total charge of the device is $+Q + (-Q) = 0$. The conductors acquire these charges when connected to the two terminals of a battery. NCERT also points out a useful idealisation — even a single conductor can be treated as a capacitor, with the second conductor imagined at infinity.
Defining Capacitance: C = Q/V
The electric field in the region between the conductors is proportional to the charge $Q$ — double the charge and the field doubles at every point, which follows directly from Coulomb's law and superposition. The potential difference $V$ is the work done per unit positive charge in carrying a test charge from one conductor to the other against this field. Since the field scales with $Q$, so does $V$. Their ratio is therefore a constant:
$$C = \frac{Q}{V}$$
This constant $C$ is the capacitance of the capacitor — the charge stored per unit potential difference. The NIOS module (Section 16.3) gives the same definition: capacitance is the ratio of the charge on either conductor to the potential difference between them, and it is a measure of the capacitor's ability to store charge. A large $C$ means the device can hold a large charge $Q$ at a relatively small voltage $V$, which is exactly what makes capacitors practically useful.
$C = Q/V$ is a fixed ratio, not a cause-and-effect
Students read $C = Q/V$ and conclude that increasing $V$ lowers $C$, or that adding charge raises $C$. Both are wrong. $Q$ and $V$ rise and fall together in lock-step, so their ratio is pinned. Charge a capacitor more and $V$ climbs by the same factor — $C$ does not budge.
$C$ is constant for a given capacitor. $Q$ and $V$ are variables tied by $Q = CV$.
The Farad and Its Submultiples
From $C = Q/V$, the SI unit of capacitance is the farad (F), where $1\ \text{F} = 1\ \text{coulomb volt}^{-1} = 1\ \text{C V}^{-1}$. A capacitor has a capacitance of one farad if a charge of one coulomb across it produces a potential difference of one volt.
Because the coulomb is itself an enormous unit of charge, the farad is a very large unit. Real capacitors almost never reach a full farad of capacitance, so engineers work in submultiples. NCERT lists the standard ones.
| Quantity | Symbol | Unit / Value | Note |
|---|---|---|---|
| Capacitance | C | farad (F) = C V⁻¹ | SI unit; defining relation $C = Q/V$ |
| Microfarad | µF | 1 µF = 10⁻⁶ F | Common in power/AC circuits |
| Nanofarad | nF | 1 nF = 10⁻⁹ F | Signal and timing circuits |
| Picofarad | pF | 1 pF = 10⁻¹² F | High-frequency / small capacitors |
The farad is huge — answers come out in µF and pF
An isolated sphere would need a radius of roughly $9 \times 10^9$ m — larger than the Sun — to reach $1$ F. So when a problem gives plate dimensions of centimetres, expect an answer in picofarads or microfarads. A "capacitance" that comes out near $1$ F from lab-scale geometry signals an arithmetic slip with the powers of ten.
Watch the exponents: $\mu = 10^{-6}$, $n = 10^{-9}$, $p = 10^{-12}$.
Why C Depends Only on Geometry
The single most tested fact about capacitance is what it depends on. NCERT states it plainly: $C$ is independent of $Q$ or $V$, and depends only on the geometrical configuration — the shape, size and separation of the two conductors — together with the nature of the insulating medium (the dielectric) between them.
This is why $Q/V$ is a constant in the first place. Fix the geometry and the medium, and the capacitor's ability to store charge is set. You can pour in more charge or apply a bigger voltage, but the proportionality $Q = CV$ holds with the same $C$. The role of the dielectric medium is developed separately, but it too is a property of the capacitor's construction, not of how it is charged.
See exactly how shape and separation set $C$ in the workhorse case — the parallel plate capacitor, where $C = \varepsilon_0 A / d$.
Isolated Spherical Conductor
The simplest worked case of "$C$ from geometry alone" is an isolated conducting sphere, with its second conductor at infinity. NIOS Section 16.3.1 derives it directly. A sphere of radius $R$ carrying charge $Q$ has potential
$$V = \frac{Q}{4\pi\varepsilon_0 R}$$
Applying $C = Q/V$, the charge cancels and we are left with a result that depends on nothing but the radius:
$$C = 4\pi\varepsilon_0 R$$
Numerically, $C$ in farad equals $R$ (in metres) divided by $9 \times 10^9$. The smallness of capacitance at lab scale is striking: a sphere of radius $0.18$ m has a capacitance of only about $20$ pF. This single relation also explains a recurring NEET pattern — for spheres carrying the same charge, the larger sphere has the larger capacitance and therefore the smaller potential.
Two hollow conducting spheres of radii $R_1$ and $R_2$ (with $R_1 \gg R_2$) carry equal charges. On which sphere is the potential higher?
For an isolated sphere $V = Q/(4\pi\varepsilon_0 R)$. With $Q$ the same on both, $V \propto 1/R$. The smaller sphere ($R_2$) has the larger potential. Equivalently, the larger sphere has the larger capacitance $C = 4\pi\varepsilon_0 R$, so it sits at a lower voltage for the same stored charge. This is NEET 2022 Q.27 verbatim.
Symbol, Working and Types
In a circuit a fixed capacitor is drawn as two short parallel lines, —||—, while a variable capacitor adds an arrow across the symbol. The working principle, as NIOS describes it, is straightforward: bringing an uncharged, earthed conductor near a charged conductor induces opposite charge on its near face, which lowers the potential of the charged conductor and so raises its capacitance. That is why a second conductor is deliberately placed close to the first — it lets the system store far more charge at the same voltage.
Capacitors come in several practical forms, distinguished mainly by the dielectric used and whether the capacitance is fixed or adjustable. NIOS Section 16.3.2 notes their use in radios, televisions, amplifiers and oscillators, as well as in power supply systems.
| Type | Capacitance | Typical Use |
|---|---|---|
| Fixed capacitor | Set value (—||—) | General storage and filtering |
| Variable capacitor | Adjustable | Tuning circuits in radio/TV |
| Parallel plate (air / paper / mica / glass) | $\varepsilon_0 A / d$ (air) | Standard laboratory capacitor |
For NEET, the depth required here is modest: recognise the symbol, understand that a second nearby conductor boosts capacitance, and know that the dielectric and geometry — never the charge — fix the value of $C$. The quantitative treatment of the most common arrangement is taken up next.
Capacitors and Capacitance in one glance
- A capacitor is two conductors separated by an insulator, carrying $+Q$ and $-Q$; the total charge is zero, and $Q$ is the charge on one conductor.
- Capacitance is the charge stored per unit potential difference: $C = Q/V$. Since $V \propto Q$, this ratio is a constant.
- SI unit is the farad, $1\ \text{F} = 1\ \text{C V}^{-1}$; practical units are $\mu\text{F}$, $n\text{F}$ and $p\text{F}$.
- $C$ is independent of $Q$ and $V$; it depends only on geometry (shape, size, separation) and the dielectric medium.
- An isolated sphere of radius $R$ has $C = 4\pi\varepsilon_0 R$, proportional to the radius alone.