Exercises: Analogue electronic components

Explain what a diode is and what it means that it conducts "in one direction only". Describe what happens when it is forward biased (anode to positive) and when it is reverse biased, using the analogy of a water non-return valve.

An LED has polarity: the anode (long lead) must go to the positive terminal. Explain what the acronym LED stands for, what happens if it is connected backwards, and why an LED does not light up even if the battery has sufficient voltage if it is incorrectly oriented.

Explain what an LDR is and how its resistance changes when going from full light to darkness (it drops significantly in light and rises significantly in the dark). Give an example of an everyday device that uses it to automatically decide whether to switch something on.

Explain what an NTC thermistor is, what it means for its coefficient to be 'negative' (as temperature rises, its resistance drops), and cite an application where measuring temperature with it is useful (thermostat, overheating warning).

Explain what a capacitor is and what it means for it to 'store charge'. State the unit used to measure its capacitance (the farad) and describe two applications: filtering a rippled voltage and timing (creating delays).

A transistor has three pins: collector, base and emitter. Using the analogy of a tap controlled by a small handle, explain how a small current through the base controls a large current between the collector and emitter.

A silicon diode starts conducting appreciably when the forward voltage exceeds about $0{,}7\ \text{V}$, its 'threshold voltage'. Explain what this threshold means and reason why a diode connected to a $1{,}5\ \text{V}$ battery with a resistor can conduct, but not with a $0{,}5\ \text{V}$ battery.

Match each component to its role in a circuit: (1) diode, (2) LED, (3) capacitor, (4) transistor, (5) LDR and (6) NTC thermistor, with: (a) allowing current to pass in only one direction; (b) indicating with light that something is active; (c) temporarily storing charge; (d) acting as an electrically controlled switch; (e) detecting the light level; (f) measuring the temperature.

It is desired to power a red LED (operating voltage $2\ \text{V}$, current $20\ \text{mA}$) from a $9\ \text{V}$ battery using a series resistor. (a) Calculate the voltage drop across the resistor. (b) Calculate the resistance value by applying Ohm's law, $R = \frac{V}{I}$, using the correct units. (c) Explain what would happen if the resistance were much smaller than calculated.

The figure shows the voltage-current characteristic curve of a silicon diode, with the threshold voltage marked with a question mark, as shown in the figure.

(a) Explain what each region of the curve represents: the almost flat region on the left and the steeply rising region on the right. (b) State the approximate value of the voltage marked with the question mark in a silicon diode and what it means. (c) Reason why the reverse current is practically zero and what happens if the breakdown voltage is exceeded.

A potential divider powered at $12\ \text{V}$ consists of an LDR at the top and a fixed resistor of $10\ \text{k}\Omega$ at the bottom, with the output taken at the midpoint. The LDR has a resistance of $2\ \text{k}\Omega$ in light and $50\ \text{k}\Omega$ in darkness. Calculate the midpoint voltage in both cases, $V_\text{salida} = 12 \cdot \frac{R_\text{fija}}{R_\text{fija} + R_\text{LDR}}$, and explain why this midpoint serves as a 'light/darkness' signal.

An NTC thermistor of $10\ \text{k}\Omega$ at $25\ ^\circ\text{C}$ drops to $5\ \text{k}\Omega$ at $45\ ^\circ\text{C}$. It is mounted in a potential divider with a fixed resistor of $10\ \text{k}\Omega$, powered at $10\ \text{V}$, with the NTC thermistor at the top and the fixed resistor at the bottom. (a) Calculate the midpoint voltage at $25\ ^\circ\text{C}$ and at $45\ ^\circ\text{C}$. (b) Explain how a circuit reading that voltage can determine whether it is hotter or colder, and why the output rises with temperature in this setup.

A $100\ \mu\text{F}$ capacitor is charged through a $10\ \text{k}\Omega$ resistor.

1. a) Calculate the time constant of the circuit, $\tau = R \cdot C$, expressed in seconds.

1. b) Explain what this value of $\tau$ physically means in the capacitor's charging process.

1. c) Explain how the delay would change if the resistance were doubled.

An NPN transistor controls an LED powered by a $9\ \text{V}$ source. The LED is connected in series with the collector of the transistor, and the base is connected to a push button through a resistor in series with it. When a small current enters the base, the transistor conducts and the LED turns on; when no current enters, the transistor does not conduct and the LED turns off.

Explain:

1. a) What role the resistor connected in series with the base plays.

1. b) How this "all or nothing" use of the transistor differs from its use as an amplifier.

The circuit in the figure is a dusk sensor: a potential divider with an LDR controls the base of a transistor that lights up an LED, with the base voltage marked with a question mark, as shown in the figure.

(a) Explain the role of each block: the LDR-R potential divider, the transistor and the LED. (b) Reason what happens to the resistance of the LDR and to the marked base voltage when transitioning from light to darkness in this setup (LDR at the top, fixed resistor at the bottom). (c) Explain why the LED lights up in only one of the two situations.

It is desired to create a light that turns on automatically at nightfall using a potential divider with an LDR and a transistor. Explain in which position of the divider (top, towards positive, or bottom, towards 0V/ground) you would place the LDR and the fixed resistor to achieve this, justifying your choice based on how the midpoint voltage varies with light.

A transformer delivers a sinusoidal AC voltage of $12\ \text{V}_\text{rms}$ at $50\ \text{Hz}$ at its secondary, connected to a half-wave rectifier consisting of a silicon diode ($V_D = 0{,}7\ \text{V}$ in conduction) in series with a load resistance of $100\ \Omega$.

(a) Accurately predict the maximum voltage value ($V_\text{peak}$) that will be reached across the terminals of the load resistor during the positive half-cycle, and justify why it differs both from the $12\ \text{V}$ RMS and from the peak value of the secondary.

(b) When connecting a capacitor in parallel with the load to stabilize the voltage, it is found that the ripple increases significantly if the ohmic value of the load is reduced to $10\ \Omega$. Justify this phenomenon physically by relating the discharge rate of the capacitor to the circuit's time constant.

(c) Design a modification to the diode topology of the circuit to halve the time between capacitor recharge pulses without altering the mains frequency, quantitatively justifying how this change will affect the final average DC voltage.

A manufacturer designs a light fitting connected to a regulated $12\ \text{V}$ power supply and considers two options to power two identical LED diodes according to catalog specifications ($V_F = 2{,}0\ \text{V}$, $I_F = 15\ \text{mA}$ each):

• Option A: Both LEDs in series with a single current-limiting resistor $R_A$.

• Option B: Both LEDs in parallel sharing a single common current-limiting resistor $R_B$.

(a) Calculate the theoretical resistance value for both options and select the next higher standard commercial value (E12 series: $100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820\ \Omega$). Furthermore, determine the minimum commercial power rating of the resistor ($1/4\ \text{W}$ or $1/2\ \text{W}$) in each case.

(b) Due to manufacturing tolerances, one diode actually has a threshold voltage of $1{,}95\ \text{V}$ and the other of $2{,}05\ \text{V}$. Justify what will happen in the Option B setup by analyzing the $I$-$V$ characteristic curve of the diode, and predict why this configuration often triggers the premature thermal destruction of the components.

(c) If the $12\ \text{V}$ supply voltage suffers an accidental overvoltage and rises to $14\ \text{V}$, calculate the percentage increase in current that the LEDs will experience in Option A and analyze the overall energy efficiency of the system.

A twilight switch powered at $5\ \text{V}$ is designed using an NPN transistor ($V_{BE} = 0{,}7\ \text{V}$ in conduction) that must activate a $5\ \text{V} / 50\ \text{mA}$ relay connected to the collector when it gets dark. An LDR is available whose resistance varies between $2\ \text{k}\Omega$ (in full sunlight) and $50\ \text{k}\Omega$ (in total darkness), along with a fixed biasing resistor $R_1$.

(a) Design the schematic of the base voltage divider so that the circuit activates the load in the absence of light, and calculate the value of $R_1$ so that the transistor begins to conduct precisely at the twilight threshold, when the LDR reaches $20\ \text{k}\Omega$.

(b) A common statement claims: "The voltage at the midpoint of the divider does not change when connected to the base of the transistor." Refute this statement quantitatively or conceptually by explaining what happens at said node when $V_{BE}$ reaches $0{,}7\ \text{V}$.

(c) If the transistor gain is $\beta = 100$, prove through calculations whether in complete darkness ($R_\text{LDR} = 50\ \text{k}\Omega$) the transistor enters deep saturation ($I_B \ge I_C / \beta$) or remains in the active region, and explain the consequences this has for the operation of the relay and the transistor.

The control circuit of an automatic garage door uses a series RC circuit connected to a $12\ \text{V}$ DC power supply. The door remains open as long as the voltage across the capacitor terminals is below a logical trigger threshold of $7{,}5\ \text{V}$.

(a) From the general charging equation $V_C(t) = V_{cc} \cdot (1 - e^{-t / \tau})$, solve analytically for the time $t$ as a function of $\tau$ and calculate the exact numerical value of the time constant $\tau$ needed to achieve a delay of $8{,}0\ \text{s}$.

(b) In the stockroom you have capacitors of $47\ \mu\text{F}$, $100\ \mu\text{F}$, and $470\ \mu\text{F}$. Select the most suitable capacitor knowing that very high capacitance values in electrolytic capacitors entail noticeable parasitic leakage currents, and calculate the associated resistance $R$.

(c) Due to winter cold, the actual resistance increases by $10\ \%$ due to its temperature coefficient, and the supply voltage drops to $11\ \text{V}$. Reasonably predict and calculate the new delay time to reach the same $7{,}5\ \text{V}$ trigger threshold.

The figure shows the time response of the voltage $V_C(t)$ across a capacitor charging through a resistor $R$ from a $5\ \text{V}$ DC source.

(a) Prove mathematically why the instant marked with "?" is equivalent to $t = \tau = R \cdot C$ by calculating the exact fraction of voltage reached from $V_C(t) = 5 \cdot (1 - e^{-t/\tau})$, and deduce the initial slope of the curve at $t = 0$.

(b) Suppose that the capacitor had a residual charge that set its initial voltage to $V_C(0) = 1{,}0\ \text{V}$ before closing the circuit. Calculate the voltage value reached after a time $t = \tau$ has elapsed and describe what error this effect would introduce into a precision timer.

(c) If the resistor is replaced by another with a value of $2R$ and at the same time a second identical capacitor of capacitance $C$ is added in parallel with $C$, predict with justification what multiplying factor the total time required to consider the circuit practically charged ($5\tau$) will experience.

An NPN BJT transistor with parameters $\beta = 100$, $V_{BE} = 0{,}7\ \text{V}$, and $V_{CE,\text{sat}} = 0{,}2\ \text{V}$ is used to drive a $12\ \text{V}$, $400\ \text{mA}$ DC motor from the $5\ \text{V}$ digital output of a microcontroller.

(a) A designer places a base resistor $R_B = 10\ \text{k}\Omega$ arguing that, since $\beta = 100$, the base current supplied will be enough for the motor to receive its $400\ \text{mA}$. Prove by calculating the operating point ($I_B$, $I_C$, and $V_{CE}$) why this statement is false, and identify the operating region in which the transistor remains.

(b) Calculate the power dissipated by the transistor with said $10\ \text{k}\Omega$ resistor and compare it with the power dissipated if it were in deep saturation. Explain why the transistor is in imminent danger of destruction due to overheating in the first case.

(c) Design the commercial value of $R_B$ applying a safety oversaturation factor $k = 2$ ($I_B \ge 2 \cdot I_{B,\text{min}}$) to ensure that the transistor operates as an efficient closed switch.

The redesign of a standalone solar garden beacon is studied to reduce costs by eliminating the LDR and using the photovoltaic panel itself as a sensor. The system includes a small $5\ \text{V}$ solar panel, a $3{,}7\ \text{V}$ ($1200\ \text{mAh}$) rechargeable lithium battery, a Schottky diode ($V_D = 0{,}3\ \text{V}$), a PNP transistor, and a $3\ \text{V} / 25\ \text{mA}$ illumination LED.

(a) Explain the critical role of the Schottky diode placed between the solar panel and the battery, and justify what electrical consequences the battery would suffer during the night if said diode were to short-circuit due to a failure.

(b) Qualitatively design the wiring of the PNP transistor with respect to the solar panel and the battery so that, when solar radiation drops and the voltage generated by the panel decreases, the base-emitter junction of the transistor becomes forward-biased and turns on the LED automatically.

(c) Assuming that the battery is at $75\ \%$ of its usable capacity at the end of the evening and that the LED must illuminate for $9$ hours each night, calculate how many consecutive nights of autonomy (completely overcast days without recharging) the luminaire will sustain before depleting the battery.

An unregulated power supply is designed for a circuit drawing a constant current $I_L = 400\ \text{mA}$. The circuit is powered through a step-down transformer $230\ \text{V}_\text{rms} / 12\ \text{V}_\text{rms}$ ($50\ \text{Hz}$), a bridge rectifier with four silicon diodes ($V_D = 0{,}7\ \text{V}$ each), and an electrolytic filter capacitor.

(a) Calculate the peak maximum voltage value ($V_\text{pico}$) obtained at the output of the bridge rectifier and explain why two diodes contribute to the total voltage drop during each half-cycle.

(b) The circuit requires the peak-to-peak ripple voltage not to exceed $5\ \%$ of the output peak voltage. Using the constant-current discharge approximation ($V_\text{rizado} \approx \frac{I_L}{f_\text{rec} \cdot C}$), justify what the frequency $f_\text{rec}$ of the rectified pulses is and calculate the minimum commercial capacitance needed for the filter capacitor.

(c) If one of the diodes in the bridge fails open-circuit due to breakdown, quantitatively analyse how the ripple frequency, the peak-to-peak ripple amplitude, and the risk of the instantaneous minimum voltage dropping below the circuit's operational limit will change.

Topic Challenge. Design an intelligent twilight control system for a solar streetlight in your municipality, optimizing its turn-on behavior based on real light conditions.

1. Data collection: Visit the AEMET or SIAR website and check the average solar radiation in your province at dusk to estimate the critical illuminance threshold ($lux$).

2. Design and simulation: Open Tinkercad Circuits and build a circuit powered at $5\text{ V}$ consisting of a voltage divider with a photoresistor ($LDR$) and a potentiometer, connected to the base of an NPN transistor that switches between cutoff and saturation to activate an LED, protecting the base with a resistor.

3. Testing and characterization: Simulate different light levels. Record the base-emitter voltage ($V_{BE}$) and collector current ($I_C$) versus illuminance in LibreOffice Calc, plotting the curve showing the triggering around $V_{BE} \approx 0,7\text{ V}$.

4. Technical report: Prepare a brief report (one page) with screenshots of the schematic, the graph, and a reasoned proposal justifying the function of each analog component used.

Assessment criteria:

• Rigorous use of official climatic data to set the threshold.

• Correct sizing and biasing of the transistor in Tinkercad.

• Clarity of the graph ($V_{BE}$ vs. light) and precision in identifying switching.

• Functional justification of resistors, potentiometer, LDR, and diodes in the report.