r/Example 29.
be very large. First, the air’s resistance is large, soV =IRre-
quires a large voltage. We can also reason that all the energy
in the magnetic field is being dissipated in a short time, so the
power dissipated in the spark,P=IV, is large, and this requires
a large value ofV. (Iisn’t large — it is decreasing from its initial
value.) Yet a third way to reach the same result is to consider the
equationVL= dI/dt: since the time constant is short, the time
derivative dI/dtis large.
This is exactly how a car’s spark plugs work. Another application
is to electrical safety: it can be dangerous to break an inductive
circuit suddenly, because so much energy is released in a short
time. There is also no guarantee that the spark will discharge
across the air gap; it might go through your body instead, since
your body might have a lower resistance.A spark-gap radio transmitter example 29
Figure r shows a primitive type of radio transmitter, called a spark
gap transmitter, used to send Morse code around the turn of the
twentieth century. The high voltage source, V, is typically about
10,000 volts. When the telegraph switch, S, is closed, the RC
circuit on the left starts charging up. An increasing voltage differ-
ence develops between the electrodes of the spark gap, G. When
this voltage difference gets large enough, the electric field in the
air between the electrodes causes a spark, partially discharging
the RC circuit, but charging the LC circuit on the right. The LC
circuit then oscillates at its resonant frequency (typically about 1
MHz), but the energy of these oscillations is rapidly radiated away
by the antenna, A, which sends out radio waves (chapter 11).
Discussion Questions
A A gopher gnaws through one of the wires in the DC lighting system
in your front yard, and the lights turn off. At the instant when the circuit
becomes open, we can consider the bare ends of the wire to be like the
plates of a capacitor, with an air gap (or gopher gap) between them. What
kind of capacitance value are we talking about here? What would this tell
you about theRCtime constant?624 Chapter 10 Fields