Physics notes, chapter 5

Electronics

Textbook Physics Form 5 (DLP), pages 172–197

What this chapter covers

Explain thermionic emission and the production and properties of cathode rays (5.1.1, 5.1.2)
Calculate the maximum velocity of an electron accelerated across a potential difference using eV = ½mv² (5.1.3)
Explain the function of a semiconductor diode and forward and reverse bias (5.2.1)
Explain half-wave and full-wave rectification and how a capacitor smooths the output (5.2.2)
Describe the terminals and circuits of npn and pnp transistors (5.3.1)
Explain how a transistor acts as a current amplifier and calculate the amplification factor (5.3.1)
Explain how a transistor with a potential divider works as a light-controlled and a heat-controlled automatic switch (5.3.2)

5.1Electron

Thermionic emission is the emission of free electrons from a heated metal surface. Cathode rays are beams of electrons moving at high speed in a vacuum.

A metal such as a tungsten filament has many free electrons. When the filament is heated by a 6 V supply, the electrons gain enough kinetic energy to leave the metal surface. An extra high tension (E.H.T.) supply then makes the anode positive, so the emitted electrons are pulled across to it as a fast beam, which completes the circuit and gives a reading on the milliammeter.

Vacuum tube with a heated tungsten filament, cathode, anode, electron beam, 6 V supply and E.H.T. supply with milliammeter — Thermionic emission and the production of cathode rays. (Textbook Figure 5.1, p. 174)

Figure: Physics Form 5 (DLP) textbook, Figure 5.1, p. 174.

The tube is a vacuum so that the electrons are not stopped by air molecules; they reach the anode with no energy loss and at maximum speed.
If the E.H.T. connection is reversed, the milliammeter shows no reading: the anode no longer attracts the electrons.

Properties of cathode rays

Apparatus	Observation	Conclusion
Maltese cross tube	A sharp shadow of the cross on the fluorescent screen	Cathode rays travel in straight lines
Maltese cross tube	The screen glows where the rays strike it	Cathode rays cause fluorescence and carry energy
Deflection tube	The beam bends towards the positive plate in a curved (parabolic) path	Cathode rays are negatively charged
Maltese cross tube with a magnet	The shadow moves; the direction follows Fleming's left-hand rule	Cathode rays are deflected by a magnetic field

Never touch the metal parts of a deflection tube or Maltese cross tube while the E.H.T. is on, and switch the E.H.T. off when no observation is being made.

Velocity of an electron

The electrical potential energy gained by an electron crossing a potential difference V is eV. In a vacuum all of it becomes kinetic energy:

eV = ½ m v_max², so v_max = √(2eV / m)
e = 1.6 × 10⁻¹⁹ C, m = 9.11 × 10⁻³¹ kg

Worked example

An electron is accelerated from the cathode to the anode through 550 V. Find its kinetic energy and its maximum velocity.

Kinetic energy = eV = 1.6 × 10⁻¹⁹ × 550 = 8.8 × 10⁻¹⁷ J.

v_max = √(2 × 8.8 × 10⁻¹⁷ / 9.11 × 10⁻³¹) = 1.39 × 10⁷ m s⁻¹.

Because v is proportional to √V, making V four times larger only doubles the velocity.

What is the maximum velocity of an electron accelerated through 800 V?

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eV = 1.6 × 10⁻¹⁹ × 800 = 1.28 × 10⁻¹⁶ J. v = √(2 × 1.28 × 10⁻¹⁶ / 9.11 × 10⁻³¹) = 1.68 × 10⁷ m s⁻¹.

5.2Semiconductor diode

A semiconductor diode is an electronic component that allows current to flow in one direction only. It is made by joining a p-type and an n-type semiconductor to form a p-n junction.

In p-type material the majority charge carriers are holes (positive); in n-type they are electrons. Foreign atoms are added to pure semiconductor by doping.

	Forward biased	Reverse biased
Connection	Positive terminal to anode (p), negative to cathode (n)	Positive terminal to cathode, negative to anode
Depletion layer	Becomes thinner	Becomes thicker
Resistance of diode	Very small	Very high
Current and bulb	Current flows; bulb lights	No current; bulb does not light

Rectification

Rectification is the process of converting alternating current (a.c.) into direct current (d.c.).

Half-wave rectifier circuit with one diode and the input sine wave and output with only positive half cycles — Half-wave rectification: only the positive half cycles pass. (Textbook Figure 5.8, p. 184)

Figure: Physics Form 5 (DLP) textbook, Figure 5.8, p. 184.

Full-wave rectification uses four diodes in a bridge rectifier. Both half cycles are made to flow the same way through the load.

Bridge rectifier of four diodes D1 to D4 with arrows showing current through the load in the positive half cycle — Positive half cycle: D₁ and D₂ conduct, D₃ and D₄ block. In the negative half cycle D₃ and D₄ conduct. (Textbook Figure 5.9, p. 184)

Figure: Physics Form 5 (DLP) textbook, Figure 5.9, p. 184.

Smoothing with a capacitor

The rectified output is d.c. but it rises and falls. A capacitor connected in parallel with the load R smooths it: it charges and stores energy while the potential difference rises, and discharges through R while the potential difference falls, so the output does not drop to zero.

Half-wave and full-wave rectifier circuits with a capacitor in parallel with the load and the smoothed output graphs — Smoothing of half-wave and full-wave output. (Textbook Figure 5.12, p. 186)

Figure: Physics Form 5 (DLP) textbook, Figure 5.12, p. 186.

The capacitor goes in parallel with the load, not in series. A larger capacitance gives a smoother output.

One of the four diodes in a bridge rectifier burns out and stops conducting. What happens to the output?

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The circuit behaves like a half-wave rectifier: one half cycle of every cycle is missing, so there is a gap between pulses in the output.

5.3Transistor

A transistor has three terminals: the emitter (E) supplies charge carriers, the base (B) is a thin layer that controls the flow, and the collector (C) receives them.

There are two types, npn and pnp. In the symbol the arrow is on the emitter: it points out (B to E) for npn and in (E to B) for pnp. In a pnp circuit the battery polarity of both the base and collector circuits is reversed, so all the currents reverse too.

Transistor circuits with an npn transistor and a pnp transistor, each with a base circuit and a collector circuit — A transistor circuit has a base circuit (small I_B) and a collector circuit (large I_C). (Textbook Figure 5.13, p. 188)

Figure: Physics Form 5 (DLP) textbook, Figure 5.13, p. 188.

With no base current (I_B = 0) there is no collector current, so the lamp in the collector circuit stays off.
The base resistor R_B is large to limit I_B and stop the transistor overheating.
A minimum base-emitter voltage V_BE is needed: 0.7 V for silicon and 0.3 V for germanium.

Transistor as a current amplifier

A small change in I_B gives a large change in I_C. The graph of I_C against I_B is a straight line through the origin; its gradient is the amplification factor:

β = I_C / I_B (the gradient of the I_C–I_B graph)

In the textbook graph the gradient is 78.0 mA / 0.5 mA = 156, so a 1 mA change in the base current causes a 156 mA change in the collector current.

Transistor as an automatic switch

No current flows in the collector circuit unless a base current flows, so the transistor can switch a lamp, LED or bell on and off. A potential divider supplies the base voltage:

V_out = R₂ / (R₁ + R₂) × V_in

Switch	Sensor	When it switches on
Light-controlled (street light)	Light-dependent resistor (LDR): resistance high in the dark, low in bright light	In the dark R_LDR is large, so V_LDR rises above V_BE; I_B flows and the lamp lights
Heat-controlled (alarm)	Thermistor: resistance falls as temperature rises	When hot, the thermistor voltage falls, so the voltage across the fixed resistor R rises above V_BE; I_B flows and the bell rings

Light-controlled switch circuit with a 10 kilohm resistor, an LDR, a 1 kilohm base resistor, an npn transistor and a lamp on a 6 V supply — Light-controlled switch: the LDR is the lower part of the potential divider. (Textbook Figure 5.18, p. 191)

Figure: Physics Form 5 (DLP) textbook, Figure 5.18, p. 191.

Temperature-controlled alarm circuit with a thermistor above a 10 kilohm resistor, a 1 kilohm base resistor, an npn transistor and a lamp — Heat-controlled switch: the thermistor is the upper part of the divider. (Textbook Figure 5.19, p. 191)

Figure: Physics Form 5 (DLP) textbook, Figure 5.19, p. 191.

Always ask: which part of the divider is the sensor, and does its voltage go up or down when the condition changes? Swapping the sensor and the resistor reverses the behaviour (a thermistor in the lower position gives a frost alarm).

Worked example

In a light-controlled circuit V_in = 6 V and the fixed resistor is 10 kΩ. In the dark the LDR is 100 kΩ. Find V_LDR.

V_LDR = 100 / (10 + 100) × 6 = 5.45 V, well above 0.7 V, so the transistor turns on.

Why does a street-light circuit use a large resistor (for example 1 kΩ) in the base circuit?

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It limits the base current so the transistor does not become too hot and burn out.