Concept explainers
A simple relaxation oscillator circuit is shown in Fig. 7.145. The neon lamp fires when its voltage reaches 75 V and turns off when its voltage drops to 30 V. Its resistance is 120 Ω when on and infinitely high when off.
- (a) For how long is the lamp on each time the capacitor discharges?
- (b) What is the time interval between light flashes?
(a)
Calculate the discharge time of the capacitance when the lamp is on in the given circuit of Figure 7.145.
Answer to Problem 85P
The discharge time of the capacitance is
Explanation of Solution
Given data:
The neon lamp is on when its voltage reaches 75 V and turn off when its voltage drops to 30 V.
The resistance is
Refer to Figure 7.145 in the textbook.
The value of capacitance
Formula used:
Write the general expression to find the complete voltage response for an RC circuit.
Here,
Write the expression to find the time constant for an RC circuit.
Here,
C is the capacitance of the capacitor.
Calculation:
The neon lamp is on when it reaches 75 V. Therefore, the initial capacitor voltage
The neon lamp is off when it drops to 30 V. Therefore, the final capacitor voltage
When the neon lamp on and off, during that time a
Substitute
Substitute the units
Substitute
When the neon lamp is off, the voltage drops to 30 V. That is,
At
Substitute
Taking ln on both sides of the equation.
Rearrange the equation as follows,
Reduce the equation as follows,
Conclusion:
Thus, the discharge time of the capacitance is
(b)
Calculate the time interval between the light flashes.
Answer to Problem 85P
The time interval between the light flashes is
Explanation of Solution
Figure 1 shows the Thevenin resistance at the capacitance terminal.
In Figure 1, the Thevenin resistance
Substitute
Substitute the units
At
At
Dividing the equation (6) by (7).
Consider the time interval is,
Substitute
Consider the neon lamp is on when its voltage
Substitute 75 V for
Taking ln on both sides of the equation.
Since, the time interval must be taken as positive value. Therefore,
Conclusion:
Thus, the time interval between the light flashes is
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Chapter 7 Solutions
Fundamentals of Electric Circuits
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- Delmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage Learning