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Capacitance & Dielectrics

01Capacitance & Dielectrics

Capacitance

This section covers the definition of capacitance, the relationship between charge and potential difference, and the units used for capacitance.

What is capacitance?

Capacitance, CC, is the charge stored per unit potential difference.

C=QVC=\frac{Q}{V}

For a parallel plate capacitor, QQ is the magnitude of the charge on either plate and VV is the potential difference between the plates.

The plates carry equal and opposite charges, +Q+Q and −Q-Q. The quoted stored charge therefore refers to the magnitude on one plate rather than a net charge on the whole capacitor.

The circuit symbol consists of two parallel lines representing the plates.

The SI unit of capacitance is the farad (F). One farad is large for many practical capacitors, so smaller units are commonly used.

Unit Symbol In farads
microfarad μF\mu\text{F} 10−6 F10^{-6}\text{ F}
nanofarad nF\text{nF} 10−9 F10^{-9}\text{ F}
picofarad pF\text{pF} 10−12 F10^{-12}\text{ F}

Worked example: For a capacitor with C=1.0 nFC=1.0\,\text{nF} and an applied p.d. of 0.30 kV0.30\,\text{kV}, determine QQ.

First convert both quantities to SI units:

C=1.0×10−9 F,V=0.30×103 VC=1.0\times10^{-9}\text{ F},\qquad V=0.30\times10^3\text{ V}

Rearranging the capacitance equation gives:

Q=CVQ=CV

Hence:

Q=(1.0×10−9)(0.30×103)=3.0×10−7 CQ=(1.0\times10^{-9})(0.30\times10^3) =3.0\times10^{-7}\text{ C}

Therefore, Q=300 nCQ=300\,\text{nC}.

Exam Tip: When using C=Q/VC=Q/V for a parallel plate capacitor, QQ is the magnitude of charge on one plate. Do not add the magnitudes of the two opposite plate charges.

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