Electrical Energy
and Capacitance
Capacitance
Capacitors and Charge Storage
• Capacitor – acts as a storehouse of charge and
energy
– Typically consists of two metal plates separated by a
small distance
• Called a parallel plate capacitor
– When connected to a battery, charge is transferred
from one plate to another until the potential difference
of the capacitor is equal to the potential difference of
the battery
• The two plates will have equal and opposite charges
Capacitors and Charge Storage
Capacitors and Charge Storage
• Capacitance – the ability of a conductor to store
energy in the form of electrically separated
charges
– Ratio of charge to potential difference
– Measured in farads (F)
• Equivalent to a coulomb/volt (C/V)
• Named in honor of Michael Faraday who contributed greatly
to our knowledge of electromagnetism
• Capacitors typically range from microfarads (106) to picofarads (10-12) in strength
Capacitors and Charge Storage
• Capacitance = (magnitude of charge) /
(potential difference)
• C=Q/ΔV
• Capacitance for a parallel-plate capacitor
in a vacuum
• Capacitance = (permittivity of a vacuum) *
(area of one of the plates) / (distance
between the plates)
Capacitors and Charge Storage
• C=ε0 * A / d
• ε (lowercase sigma) represents permittivity of a
medium
– The subscript 0 means that the medium is a vacuum
• Permittivity has a value of 8.85*10-12C2/N*m2
• Capacitance decreases with increasing distance
• Capacitance increases with increasing size of
the capacitor
– Earth is so massive it is a excellent capacitor
• Used for grounding
• Can take a lot of charge without changing electric potential
Capacitors and Charge Storage
• The material between the plates can change the
capacitance
• By inserting an insulating material called a
dielectric (such as air, rubber, glass, or waxed
paper) between the plates, the capacitance
increases
– Surface charges build up on the dielectric and reduce
the charge on the plates
• More charge can be stored
• Charge is rapidly released when discharged by a
capacitor
– Discharged by connecting the plates with a conductor
Capacitors and Charge Storage
Energy and Capacitors
• Electrical potential energy stored in a charged capacitor
• Electric potential energy = ½ * (charge on one plate) *
(final potential difference)
• PEelectric = ½QΔV
• The greater the charge on the plates, the more work and
therefore energy that is needed to move charges
between the plates
• Other forms of the equation
• PEelectric = ½CΔV2
• PEelectric = Q2 / 2C
• Capacitors have a maximum energy and charge they can
store
– Exceeding this maximum causes electrical breakdowns
Energy and Capacitors