(a) Explain what is meant by the statement: The capacitance of a parallel-plate capacitor is 2\(\mu\)F (b) State: (i) three factors on which its capacitance...
(a) Explain what is meant by the statement: The capacitance of a parallel-plate capacitor is 2\(\mu\)F
(b) State: (i) three factors on which its capacitance depends
(ii) three uses of capacitors.
(c) Derive a formula for the energy W stored in a charged capacitor of capacitance C carrying a charge Q on either plate.,
(d) Two parallel-plate capacitors of capacitances 2\(\mu\)F and 3\(\mu\)F are connected in parallel and the combination is connected to a 50V d.c. source. Draw the circuit diagram of the arrangement and determine the:
(i) charge on either plate of each capacitor
(ii) potential difference across each capacitor
(iii) energy of the combinad capacitors.
(a) Meaning of \(2\,\mu\text{F}\)
Capacitance is defined by \(C=\dfrac{Q}{V}\). A capacitance of \(2\,\mu\text{F}\) means that the capacitor stores \(2\,\mu\text{C}\) of charge on each plate for every \(1\,\text{V}\) potential difference across its plates:
\[C=2\,\mu\text{F}=2\times10^{-6}\,\text{F}\]
Thus, when \(V=1\,\text{V}\), \(Q=CV=2\times10^{-6}\,\text{C}=2\,\mu\text{C}\). The two plates carry equal charges of opposite sign.
(b)(i) Factors affecting the capacitance of a parallel-plate capacitor
The area of overlap of the plates: larger area gives greater capacitance.
The separation between the plates: greater separation gives smaller capacitance.
The permittivity of the dielectric between the plates: a dielectric with higher permittivity gives greater capacitance.
For parallel plates, this is summarised by:
\[C=\frac{\varepsilon A}{d}\]
(b)(ii) Uses of capacitors
Storing charge or energy, for example in a camera flash.
Smoothing the output from a rectifier in a power supply.
Separating a.c. signals from d.c. components in electronic circuits.
(c) Derivation of the energy stored
During charging, the potential difference is not constant: it rises from \(0\) to its final value \(V\). When the charge already on the capacitor is \(q\),
\[V=\frac{q}{C}\]
The work done in bringing a further small charge \(\mathrm{d}q\) onto the capacitor is:
Examination reminder: In parallel, the potential difference is the same across every capacitor, while the charge on each capacitor is found separately using \(Q=CV\).
Capacitance is defined by \(C=\dfrac{Q}{V}\). A capacitance of \(2\,\mu\text{F}\) means that the capacitor stores \(2\,\mu\text{C}\) of charge on each plate for every \(1\,\text{V}\) potential difference across its plates:
\[C=2\,\mu\text{F}=2\times10^{-6}\,\text{F}\]
Thus, when \(V=1\,\text{V}\), \(Q=CV=2\times10^{-6}\,\text{C}=2\,\mu\text{C}\). The two plates carry equal charges of opposite sign.
(b)(i) Factors affecting the capacitance of a parallel-plate capacitor
The area of overlap of the plates: larger area gives greater capacitance.
The separation between the plates: greater separation gives smaller capacitance.
The permittivity of the dielectric between the plates: a dielectric with higher permittivity gives greater capacitance.
For parallel plates, this is summarised by:
\[C=\frac{\varepsilon A}{d}\]
(b)(ii) Uses of capacitors
Storing charge or energy, for example in a camera flash.
Smoothing the output from a rectifier in a power supply.
Separating a.c. signals from d.c. components in electronic circuits.
(c) Derivation of the energy stored
During charging, the potential difference is not constant: it rises from \(0\) to its final value \(V\). When the charge already on the capacitor is \(q\),
\[V=\frac{q}{C}\]
The work done in bringing a further small charge \(\mathrm{d}q\) onto the capacitor is:
Examination reminder: In parallel, the potential difference is the same across every capacitor, while the charge on each capacitor is found separately using \(Q=CV\).
