Energy and Human Ambitions on a Finite Planet, 2021a

5 <strong>Energy</strong> <strong>and</strong> Power Units 77
Voltage is a measure of electric potential, inVolts, <strong>and</strong> can be thought
of as analogous to how high something is lifted. 28 A higher voltage is
like sitting higher on the shelf, <strong>and</strong> can do more work if allowed to be
released.
28: . . . making electric potential a lot like
gravitational potential energy in flavor
Charge is moved around by electrical forces, <strong>and</strong> the amount of charge
moved plays a role similar to that of mass in gravitational settings. The
unit of charge is the Coulomb (C), <strong>and</strong> the smallest unit of charge we
encounter in normal situations is from the proton (+1.6 × 10 −19 C) or
the electron (−1.6 × 10 −19 C).
Definition 5.8.1 The amount of energy in a charge, q, at a voltage, V,is
E qV. (5.1)
One Coulomb of charge at a potential of 1 V has an energy of 1 J.
Current is the rate at which charge flows, <strong>and</strong> is usually symbolized by
the letter I. Imagine setting up a toll booth in a conducting wire <strong>and</strong>
counting how many charges (or how much cumulative charge) pass the
gate per unit time. This gives rise to the Definition 5.8.2.
Definition 5.8.2 Current is measured in Amps, 29 which is defined as one
Coulomb per second.
29: Amperes, formally
Moving one Coulomb through one Volt every second would constitute
one Joule of energy every second, which is the definition of one Watt.
Putting the concepts of Definition 5.8.1 <strong>and</strong> Definition 5.8.2 together, we
find ourselves able to define electrical power.
Definition 5.8.3 Electrical power is simply current multiplied by voltage:
Current, I,isinAmps, <strong>and</strong> voltage, V is in Volts.
P IV. (5.2)
Example 5.8.1 Households in the U.S. often have circuit breakers
allowing maximum currents of 15 or 20 Amps for regular power
outlets. At a voltage of 120 V, 30 this corresponds to a maximum power
of 1,800 W or 2,400 W, respectively. 31
Finally, we are in a position to underst<strong>and</strong> how much energy a battery will
hold. Batteries are rated by two numbers: voltage, <strong>and</strong> charge capacity.
Since current is charge per time, multiplying current <strong>and</strong> time results in
just charge. 32 Therefore, charge capacity in batteries is characterized as
Amp-hours (Ah) or milli-amp-hours (mAh). Since Amps times Volts is
Watts (Eq. 5.2), Amp-hours times Volts is Watt-hours, a familiar unit of
energy from Section 5.4.
30: The alternating current nature is already
accommodated in this measure of
voltage.
31: Safety regulations limit continuous use
to 80% of the breaker current capacity, so
that realistically the limits are 1,400 W <strong>and</strong>
1,920 W, respectively. This is why “heating
appliances” in Figure 5.2 top out around
1,500 W: circuit/safety limits.
32: For example, 0.1 Amps (0.1 Coulombs
per second) of current sustained for a duration
of 100 seconds results in 10 Coulombs
of charge flow.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.