Physics · Chapter 22
Study notes aligned to the official NEB syllabus.
A capacitor is an electronic device used to store electric charge and, with it, electrical energy. In its simplest form a capacitor consists of two conducting plates separated by an insulating (dielectric) medium such as air, paper, mica, or a thin plastic film.
When the plates are connected to a battery, charge $+Q$ collects on one plate and an equal and opposite charge $-Q$ on the other, setting up an electric field and a potential difference between the plates. Capacitors are widely used in practical circuits: for smoothing (filtering) the output of rectifiers in power supplies, for tuning radio and television receivers, in timing and oscillator circuits, as energy stores in camera flash units, and for blocking direct current while passing alternating current.
This chapter defines capacitance, derives the capacitance of a parallel plate capacitor, works out the equivalent capacitance of series and parallel combinations, deduces the energy stored in a charged capacitor, and explains the effect of a dielectric.
Experiment shows that the charge $Q$ stored on a capacitor is directly proportional to the potential difference $V$ applied across its plates:
$$Q \propto V \quad\Rightarrow\quad Q = CV$$
The constant of proportionality $C$ is called the capacitance of the capacitor.
Capacitance is defined as the ratio of the charge stored on either plate to the potential difference between the plates:
$$C = \frac{Q}{V}$$
More precisely, capacitance is the ratio of the change in charge in a system to the corresponding change in its electric potential, and it measures the ability of the system to store charge. A large capacitance means a large charge can be stored for only a small rise in potential difference.
If $V = 1\ \text{volt}$, then $C = Q$ numerically. Thus the capacitance of a capacitor is numerically equal to the charge required to raise its potential difference by one volt.
SI unit. The SI unit of capacitance is the farad (F), where
$$ \begin{aligned} 1\ \text{farad} &= \frac{1\ \text{coulomb}}{1\ \text{volt}} \ \qquad 1\ \text{F} &= 1\ \text{C V}^{-1} \end{aligned} $$
The farad is a very large unit, so practical capacitors are rated in submultiples:
$$ \begin{aligned} 1\ \mu\text{F} &= 10^{-6}\ \text{F} \ \qquad 1\ \text{nF} &= 10^{-9}\ \text{F} \ \qquad 1\ \text{pF} &= 10^{-12}\ \text{F} \end{aligned} $$
The value of $C$ depends only on the geometry of the plates (their area and separation) and on the nature of the dielectric between them, not on the charge or voltage.
Rearranging $Q = CV$ gives a linear relation between the charge $Q$ stored and the potential difference $V$:
$$V = \frac{1}{C},Q$$
A graph of potential difference $V$ (vertical axis) against charge $Q$ (horizontal axis) is therefore a straight line through the origin with gradient $\dfrac{1}{C}$:
$$ \begin{aligned} \text{gradient of } V\text{-}Q \text{ graph} &= \frac{V}{Q} \ &= \frac{1}{C} \end{aligned} $$
Equivalently, a graph of charge $Q$ against potential difference $V$ is a straight line whose gradient is the capacitance $C$ itself:
$$ \begin{aligned} \text{gradient of } Q\text{-}V \text{ graph} &= \frac{Q}{V} \ &= C \end{aligned} $$
A steeper $Q$-$V$ line means a larger capacitance.
From $C = \dfrac{Q}{V}$, for a fixed charge $Q$ the capacitance is inversely related to the potential:
$$C \propto \frac{1}{V} \quad (Q \text{ constant})$$
If the potential of a charged plate can be lowered without removing charge, its capacitance rises. This is the working principle of a capacitor: bringing an earthed conducting plate close to a charged plate (with a dielectric between them) lowers the potential of the charged plate, so a much larger charge can be stored for the same potential. This is why two closely spaced plates store far more charge than an isolated plate at the same voltage.
A parallel plate capacitor consists of two flat conducting plates, each of area $A$, held parallel to each other a small distance $d$ apart, with a dielectric (air or vacuum for the basic case) filling the gap.
A capacitor is an electronic device used to store electric charge and, with it, electrical energy. In its simplest form a capacitor consists of two conducting plates separated by an insulating (dielectric) medium such as air, paper, mica, or a thin plastic film.
When the plates are connected to a battery, charge collects on one plate and an equal and opposite charge on the other, setting up an electric field and a potential difference between the plates. Capacitors are widely used in practical circuits: for smoothing (filtering) the output of rectifiers in power supplies, for tuning radio and television receivers, in timing and oscillator circuits, as energy stores in camera flash units, and for blocking direct current while passing alternating current.
This chapter defines capacitance, derives the capacitance of a parallel plate capacitor, works out the equivalent capacitance of series and parallel combinations, deduces the energy stored in a charged capacitor, and explains the effect of a dielectric.
Experiment shows that the charge stored on a capacitor is directly proportional to the potential difference applied across its plates:
The constant of proportionality is called the capacitance of the capacitor.
Capacitance is defined as the ratio of the charge stored on either plate to the potential difference between the plates:
More precisely, capacitance is the ratio of the change in charge in a system to the corresponding change in its electric potential, and it measures the ability of the system to store charge. A large capacitance means a large charge can be stored for only a small rise in potential difference.
If , then numerically. Thus the capacitance of a capacitor is numerically equal to the charge required to raise its potential difference by one volt.
SI unit. The SI unit of capacitance is the farad (F), where
The farad is a very large unit, so practical capacitors are rated in submultiples:
The value of depends only on the geometry of the plates (their area and separation) and on the nature of the dielectric between them, not on the charge or voltage.
Rearranging gives a linear relation between the charge stored and the potential difference :
A graph of potential difference (vertical axis) against charge (horizontal axis) is therefore a straight line through the origin with gradient :
Equivalently, a graph of charge against potential difference is a straight line whose gradient is the capacitance itself:
A steeper - line means a larger capacitance.
From , for a fixed charge the capacitance is inversely related to the potential:
If the potential of a charged plate can be lowered without removing charge, its capacitance rises. This is the working principle of a capacitor: bringing an earthed conducting plate close to a charged plate (with a dielectric between them) lowers the potential of the charged plate, so a much larger charge can be stored for the same potential. This is why two closely spaced plates store far more charge than an isolated plate at the same voltage.
A parallel plate capacitor consists of two flat conducting plates, each of area , held parallel to each other a small distance apart, with a dielectric (air or vacuum for the basic case) filling the gap.