Exercises: Timers and the 555 integrated circuit

Explain what a timer is within an electronic circuit and name two everyday appliances that contain one, stating what time duration each one controls.

A capacitor charges through a resistor. Explain why the charging is not instantaneous and what happens to the charging time if the resistance value is increased.

Distinguish between an ON-delay timer and an OFF-delay timer, giving an example of the use of each type.

The graph shows two processes involving a capacitor: in one it charges through a resistor and in the other it discharges. State which curve corresponds to each process and reason why the voltage does not vary in a straight line.

The 555 is a timer in the form of an integrated circuit. Explain what an integrated circuit is and what each of the two basic 555 configurations does: astable and monostable.

In astable configuration, the 555 has no stable state: its output continuously changes on its own. Explain what is observed in an LED connected to that output and give two applications of this behaviour.

In monostable configuration, the 555 outputs a single pulse of fixed duration when it receives a trigger signal. Explain the complete cycle of a staircase light set up in this way: what happens when the button is pressed and what happens when the time expires.

The time constant of an RC circuit is $\tau = R \cdot C$. Without doing any calculations, reason what happens to $\tau$ and to the timer rhythm if the capacitance of the capacitor is doubled, and what happens if the resistance is doubled.

Describe how the current and voltage evolve during the charging of a capacitor through a resistor: why charging is fast at first and then slows down, and what value the capacitor voltage reaches at the end of the process.

A bathroom extractor fan keeps running for a few minutes after turning off the light (OFF-delay). Explain what role a charged capacitor can play in this behaviour and what would change if its capacitance were doubled.

The diagram shows a flasher circuit using the 555 in astable configuration: the output turns the LED on and off at a rate set by two resistors and a capacitor. One of the components is marked with ?. Identify which one it is and explain what would happen to the flashing rate if its value were twice as large.

A car indicator is an astable circuit. Explain why the flashing rate depends on the timing components, and reason why, when one of the bulbs blows, the indicator usually flashes faster (what has changed in the circuit).

An RC circuit has a resistor $R = 10\ \text{k}\Omega$ and a capacitor $C = 100\ \mu\text{F}$. Calculate the time constant $\tau = R \cdot C$ in seconds and reason what type of delay this timer could be used for.

A dishwasher waits a few minutes before starting after closing the door (ON-delay), while the bathroom fan continues running for a while after turning off the light (OFF-delay). Draw or describe the two timelines (what the output does at each instant) and explain the difference between both delays.

You can do it on paper and send a photo with your answer.

In an astable circuit, the LED is on for a certain time and off for another. Explain the relationship between these two time durations and the timing resistors, and how you would achieve a flashing effect where the ON-time is much longer than the OFF-time.

A buzzer with a 555 monostable sounds for 5 seconds even if the push button is released instantly. Describe the complete cycle (trigger, pulse and return to rest) and explain why the circuit "ignores" the push button during those 5 seconds.

The attached graph shows the charging of the same capacitor with capacitance $C = 220\ \mu\text{F}$ through two different resistors ($R_1$ and $R_2$), powered at $9\ \text{V}$. A classmate claims that curve 1 corresponds to the larger resistor "because it rises with a steeper slope since it has a stronger resistor", and also that after $\tau_1$ seconds the capacitor has already reached half of its final voltage (4,5 V).

1. a) Reasonably refute both statements based on the physical definition of the time constant ($\tau = R \cdot C$) and the interpretation of the graph.
2. b) If it is verified from the graph that $\tau_1 = 2,2\ \text{s}$ and that $\tau_2$ is exactly double, calculate the ohmic value of $R_1$ and $R_2$.
3. c) If this circuit is used to trigger a transistor that switches when the voltage across the capacitor reaches exactly $4,5\ \text{V}$, estimate from the graph which of the two resistors will delay switching on more, and determine graphically at what approximate fraction of $\tau$ switching occurs.

You need to design the control module for the warning light signal of a school pedestrian crossing. Two lights are required to flash alternately and uninterruptedly at a frequency of exactly $1\ \text{Hz}$ (one complete cycle per second).

1. a) Justify whether you should configure the 555 integrated circuit in monostable or astable mode.
2. b) If you have an electrolytic capacitor with $C = 10\ \mu\text{F}$ and you set $R_A = 1\ \text{k}\Omega$ by design, calculate the theoretical value of $R_B$ knowing that the oscillation period is given by $T \approx 0,7 \cdot (R_A + 2R_B) \cdot C$.
3. c) After assembling it on the breadboard, you find that the circuit oscillates at twice the expected speed ($2\ \text{Hz}$). Predict what practical adjustment you should make to the passive components (without changing the supply voltage) to correct the offset and achieve exact calibration.

You have assembled an astable circuit with a 555 timer on a breadboard to make an LED oscillate at 1 Hz, but when you connect the power supply, the LED stays permanently lit without ever blinking.

1. a) Knowing that the 555 switches by comparing the capacitor voltage between $\frac{1}{3}V_{cc}$ and $\frac{2}{3}V_{cc}$, formulate two different fault hypotheses in the $RC$ network (at pins 2, 6, or 7) that would prevent the capacitor from charging or discharging periodically.
2. b) Design a step-by-step diagnostic protocol using only a multimeter in voltmeter mode to confirm which of the two hypotheses is causing the failure, indicating what voltage reading you expect in each case.
3. c) When measuring with an oscilloscope, you discover that the output (pin 3) switches correctly between 0 V and 9 V, but it does so at $2\ \text{kHz}$. Explain why you perceived the LED as "always on" and deduce what mistake you made when choosing the timing capacitor.

The direct current motor of an industrial model ramp breaks down frequently because the jerk from the starting torque damages the reduction gears. To solve this, you need to design an on-delay timer circuit using an $RC$ circuit and an NPN transistor that energizes a control relay.

1. a) Explain the sequence of operation from the moment the user switches on the main switch: why does the transistor base not receive sufficient current immediately, and how does the voltage evolve until switching occurs?
2. b) If you use a capacitor $C = 100\ \mu\text{F}$ and obtain a delay of $3,5\ \text{s}$ with a fixed resistor of $47\ \text{k}\Omega$, calculate the value the resistor should have if the safety department requires increasing the delay to $7\ \text{s}$.
3. c) Design a modification to the previous circuit that allows the operator to continuously calibrate the delay time between $2\ \text{s}$ and $10\ \text{s}$, indicating what specific commercial component you would add and what risk the transistor would face if said component were set to $0\ \Omega$ without a series protection resistor.

The owners' association of a 5-storey building is considering replacing the staircase lighting (10 lamps of $20\ \text{W}$ each), currently controlled by conventional manual two-way switches, with a timed system.

1. a) The lamps are left on by mistake for an average of 5 hours a day. If they are replaced with a monostable circuit with pushbuttons that turns off the light after 2 minutes, and the staircase is used 40 times a day, calculate the daily energy consumption of both systems (in $\text{Wh}$) and the percentage of savings achieved.
2. b) A neighbour suggests installing an astable circuit instead of a monostable one "so that the lights turn on automatically without having to press anything". Refute their proposal technically by justifying what unwanted behaviour an astable would cause in this case.
3. c) Predict what functional problem a person with reduced mobility would experience when climbing the stairs if the monostable circuit is not of the "retriggerable" type compared to one that is, and explain what this difference consists of.

A security system for a parking barrier cascades two 555 integrated circuits: the first in a monostable configuration ($T_1 = 8\ \text{s}$) and the second in an astable configuration ($f = 2\ \text{Hz}$, with a 50% duty cycle). The output (pin 3) of the monostable is connected directly to the reset pin (pin 4, active-low reset) of the astable, whose output powers an alarm buzzer.

1. a) Plot or precisely describe the timing diagram of the system between $t = 0\ \text{s}$ and $t = 12\ \text{s}$, assuming that at $t = 1\ \text{s}$ a short trigger pulse is received at the monostable. Include the trigger signal, the monostable output, and the signal received by the buzzer.
2. b) Deduce how many audible beeps the alarm will emit in total after said trigger pulse.
3. c) Reasonably predict what would happen if a faulty sensor keeps the monostable trigger pin connected to 0 V indefinitely: will the alarm turn off after the 8 seconds set by its $RC$ network have elapsed? Justify your prediction by analysing the internal operation of the 555's TRIGGER input.

To prevent a microcontroller from shutting down abruptly due to micro-outages in the mains, a decoupling capacitor of $C = 2.200\ \mu\text{F}$ is placed in parallel with its $5\ \text{V}$ power supply, along with an indicator LED in series with a resistor $R = 1\ \text{k}\Omega$. The microcontroller enters an emergency stop if the voltage drops below $2,5\ \text{V}$.

1. a) A student calculates $\tau = R \cdot C = 2,2\ \text{s}$ and states: "Since $\tau = 2,2\ \text{s}$, the LED will turn off completely and the voltage will drop to zero exactly $2,2\ \text{s}$ after the power cut". Refute their claim by demonstrating what theoretical voltage remains in the capacitor after $1\tau$ has elapsed and how many seconds are required to consider the discharge $99\ %$ complete ($5\tau$).
2. b) Knowing that the voltage during discharge follows $V(t) = V_0 \cdot e^{-t/\tau}$ and that it drops to $50\ %$ ($2,5\ \text{V}$) when $t \approx 0,69 \cdot \tau$, determine for exactly how long the capacitor will keep the microcontroller safe before it enters emergency stop.
3. c) Predict what will happen to the discharge rate when the capacitor voltage falls below the threshold voltage of the LED ($V_d \approx 1,8\ \text{V}$), taking into account that the diode stops conducting below that value.

In the technology workshop, a 6-second timer is designed to actuate an irrigation solenoid valve powered by a battery whose voltage fluctuates between $12\ \text{V}$ (fully charged) and $9\ \text{V}$ (discharged). Two students debate whether to build it using a bistable circuit with discrete bipolar transistors or using a 555 integrated circuit in monostable mode.

1. a) Justify why the setup with discrete transistors suffers large drifts in the programmed time if the outside temperature in the garden changes or if a transistor is replaced with another one of the same model (consider the gain $\beta$ and the leakage current of the base-emitter junction).
2. b) Analyse the internal voltage divider of the 555 (three identical $5\ \text{k}\Omega$ resistors) and demonstrate mathematically why the voltage at its switching thresholds ($\%V_{cc}$) makes the timing duration completely independent of whether the battery drops from $12\ \text{V}$ to $9\ \text{V}$.
3. c) If the operator needs to double the irrigation time without buying a new capacitor of higher capacitance, deduce what modification must be made to the external timing network and reason whether it would alter the stability of the system.

Topic challenge. Design the smart lighting system for a rural bus shelter, ensuring that the light only turns on at night and for a limited time after a button is pressed.

1. Real data: Go to the AEMET website, write down the sunset time and the average cloud cover in your town to justify the need for night-time detection. Set a courtesy on-time of $t = 11,0\text{ s}$.

2. Design and calculation: In Tinkercad Circuits, combine an elementary circuit with an LDR and transistor acting as a darkness sensor, connected to the trigger pin of a 555 timer in monostable mode. Calculate the values of $R$ and $C$ using the expression $t \approx 1,1 \cdot R \cdot C$. For example, for $C = 100\,\mu\text{F}$, obtain the required commercial $R$ ($100,0\text{ k}\Omega$).

3. Simulation and validation: Build the complete schematic in Tinkercad, verify that the LED only times when there is no ambient light, and measure the real time using the simulator's stopwatch.

4. Final product: Submit a brief technical sheet (one page) with the public link to your simulation, the calculations performed, and the justification of the function of each component.

Assessment criteria:

• Mathematical correctness in dimensioning $R$ and $C$ using the 555 formula.

• Functional build in Tinkercad integrating the LDR sensor, transistor, and 555 IC.

• Clear and rigorous technical explanation of the role of each analog component.