The time period can be found from considering the equation
where
Solution
The neon lamp flashes when the voltage across the capacitor reaches 80 V. The
RC time constant is equal to
We can solve the voltage equation for the time it takes the capacitor to reach 80 V:
Significance
One application of the relaxation oscillator is for controlling indicator lights that flash at a frequency determined by the values for
R and
C . In this example, the neon lamp will flash every 8.13 seconds, a frequency of
The relaxation oscillator has many other practical uses. It is often used in electronic circuits, where the neon lamp is replaced by a transistor or a device known as a tunnel diode. The description of the transistor and tunnel diode is beyond the scope of this chapter, but you can think of them as voltage controlled switches. They are normally open switches, but when the right voltage is applied, the switch closes and conducts. The “switch” can be used to turn on another circuit, turn on a light, or run a small motor. A relaxation oscillator can be used to make the turn signals of your car blink or your cell phone to vibrate.
RC circuits have many applications. They can be used effectively as timers for applications such as intermittent windshield wipers, pace makers, and strobe lights. Some models of intermittent windshield wipers use a variable resistor to adjust the interval between sweeps of the wiper. Increasing the resistance increases the
RC time constant, which increases the time between the operation of the wipers.
Another application is the
pacemaker . The heart rate is normally controlled by electrical signals, which cause the muscles of the heart to contract and pump blood. When the heart rhythm is abnormal (the heartbeat is too high or too low), pace makers can be used to correct this abnormality. Pacemakers have sensors that detect body motion and breathing to increase the heart rate during physical activities, thus meeting the increased need for blood and oxygen, and an
RC timing circuit can be used to control the time between voltage signals to the heart.
Looking ahead to the study of ac circuits (
Alternating-Current Circuits ), ac voltages vary as sine functions with specific frequencies. Periodic variations in voltage, or electric signals, are often recorded by scientists. These voltage signals could come from music recorded by a microphone or atmospheric data collected by radar. Occasionally, these signals can contain unwanted frequencies known as “noise.”
RC filters can be used to filter out the unwanted frequencies.
In the study of electronics, a popular device known as a 555 timer provides timed voltage pulses. The time between pulses is controlled by an
RC circuit. These are just a few of the countless applications of
RC circuits.
Intermittent windshield wipers
A relaxation oscillator is used to control a pair of windshield wipers. The relaxation oscillator consists of a 10.00-mF capacitor and a
variable resistor known as a rheostat. A knob connected to the variable resistor allows the resistance to be adjusted from
to
The output of the capacitor is used to control a voltage-controlled switch. The switch is normally open, but when the output voltage reaches 10.00 V, the switch closes, energizing an electric motor and discharging the capacitor. The motor causes the windshield wipers to sweep once across the windshield and the capacitor begins to charge again. To what resistance should the rheostat be adjusted for the period of the wiper blades be 10.00 seconds?
Strategy
The resistance considers the equation
where
The capacitance, output voltage, and voltage of the battery are given. We need to solve this equation for the resistance.
Solution
The output voltage will be 10.00 V and the voltage of the battery is 12.00 V. The capacitance is given as 10.00 mF. Solving for the resistance yields
Significance
Increasing the resistance increases the time delay between operations of the windshield wipers. When the resistance is zero, the windshield wipers run continuously. At the maximum resistance, the period of the operation of the wipers is: