Timers and the 555 integrated circuit

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.

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.

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.

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

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 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.

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 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.

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 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.

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.