Is it correct to say: Writing I_C = I_E + I_B?

The emitter current is the largest: I_E = I_B + I_C.

Is it correct to say: Using β = α/(1 + α)?

β = α/(1 − α) and α = β/(1 + β). Check: α must come out less than 1, and β much greater than 1.

Is it correct to say: Taking the ripple frequency of a full-wave rectifier equal to the input frequency?

A full-wave rectifier gives two pulses per cycle, so the ripple frequency is 2f (100 Hz on 50 Hz mains).

Is it correct to say: Saying a photodiode or Zener regulator is operated in forward bias?

Both are operated in reverse bias. Only the LED among these devices is forward biased.

Is it correct to say: Forgetting the load current in Zener problems and taking I_Z = I_s?

I_Z = I_s − I_L. Only with no load connected does the whole series current flow through the Zener.

Is it correct to say: Treating XOR as OR?

For A = B = 1, OR gives 1 but XOR gives 0. XOR is 1 only when the inputs differ.

📄 Formula sheet (PDF)

Semiconductor Devices

Half-wave and full-wave rectifiers, Zener diode voltage regulator, photodiode, solar cell, LED, bipolar junction transistor (α and β) and logic gates — Maharashtra HSC Physics Ch 16

📐 12 formulas✏️ 4 examples🎯 6 practice🏫 Maharashtra State Board📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Rectifier answers need a labelled circuit diagram together with input and output waveforms. Show which diode conducts in each half cycle of a full-wave rectifier.
→For the Zener regulator, explain the mechanism in words. The Zener is reverse biased in breakdown, so the output stays at V_Z. Any change in input or load changes only the Zener current, and the series resistor drops the excess voltage.
→The derivation of the α–β relation takes three lines from I_E = I_B + I_C. Divide by I_C and use α = I_C/I_E, β = I_C/I_B.
→Know the biasing of each optoelectronic device. LED: forward biased. Photodiode: reverse biased. Solar cell: no external bias, because it generates its own emf.
→For any logic circuit, write the output of each intermediate gate as a Boolean expression, then build the truth table column by column and compare the final column with the truth tables of the basic gates.
→Watch current units in transistor numericals. Base current is usually in μA and collector current in mA, so convert before dividing.

📐 Formulas(12)

Ripple Frequency of Rectifier Output

f_{o u t} = f_{in} (half-wave), f_{o u t} = 2 f_{in} (full-wave)

Symbol	Meaning
$f_{in}$	Frequency of the AC input (Hz)
$f_{o u t}$	Frequency of the ripple in the output (Hz)

Ripple Factor

γ = \frac{V _{a c, r m s}}{V _{d c}} = \frac{rms value of AC component}{value of DC component}

Zener Regulator — Current Through Series Resistor★ Board fav

I_{s} = \frac{V _{in} - V _{Z}}{R _{s}}

Symbol	Meaning
$V_{in}$	Unregulated input voltage (V)
$V_{Z}$	Zener breakdown voltage = regulated output (V)
$R_{s}$	Series resistance (Ω)
$I_{s}$	Current through the series resistor (A)

Zener Regulator — Load and Zener Currents

I_{L} = \frac{V _{Z}}{R _{L}}, I_{Z} = I_{s} - I_{L}

Symbol	Meaning
$R_{L}$	Load resistance (Ω)
$I_{L}$	Load current (A)
$I_{Z}$	Zener current (A)

Photon Energy and Band Gap (LED, Photodiode, Solar Cell)

E_{g} = h ν = \frac{h c}{λ} \Rightarrow λ = \frac{h c}{E _{g}}

Symbol	Meaning
$E_{g}$	Band gap energy (J or eV)
$h$	Planck's constant = 6.63×10⁻³⁴ J s
$c$	Speed of light = 3×10⁸ m s⁻¹
$λ$	Wavelength of emitted or absorbed light (m)

Transistor Currents★ Board fav

I_{E} = I_{B} + I_{C}

Symbol	Meaning
$I_{E}$	Emitter current (A)
$I_{B}$	Base current (A)
$I_{C}$	Collector current (A)

Common-Base DC Current Gain

α_{d c} = \frac{I _{C}}{I _{E}}

Common-Emitter DC Current Gain

β_{d c} = \frac{I _{C}}{I _{B}}

Relation Between α and β★ Board fav

β = \frac{α}{1 - α}, α = \frac{β}{1 + β}

OR, AND and NOT Gates

OR: Y = A + B, AND: Y = A \cdot B, NOT: Y = A

NAND and NOR Gates

NAND: Y = A \cdot B, NOR: Y = A + B

XOR (Exclusive-OR) Gate

Y = A \oplus B = A B + A B

✏️ Solved Examples

1Solved Exampleeasy4 steps

In a transistor, the emitter current is 8 mA and the collector current is 7.84 mA. Find the base current, α_dc and β_dc.

Base current from I_E = I_B + I_C.

I_{B} = I_{E} - I_{C} = 8 - 7.84 = 0.16 mA

2Solved Exampleboard3 steps

A transistor in common-emitter configuration has β = 120. If the base current is 25 μA, find the collector current, the emitter current and α.

Collector current.

I_{C} = β I_{B} = 120 \times 25 \times 1 0^{- 6} = 3.0 \times 1 0^{- 3} A = 3.0 mA

3Solved Exampleboard4 steps

A Zener diode with V_Z = 9 V is used as a voltage regulator with a series resistance of 200 Ω and a load of 1.5 kΩ. The input voltage is 15 V. Find the current through the series resistor, the load current, the Zener current and the power dissipated in the Zener.

Current through the series resistor.

I_{s} = \frac{V _{in} - V _{Z}}{R _{s}} = \frac{15 - 9}{200} = 0.030 A = 30 mA

4Solved ExampleHOTS4 steps

Inputs A and B are each passed through a NOT gate, and the two outputs are fed to a NAND gate. Find the Boolean expression of the final output and identify the equivalent single gate.

The NAND gate receives Ā and B̄.

Y = A \cdot B

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Writing I_C = I_E + I_B
✓The emitter current is the largest: I_E = I_B + I_C.
2
Using β = α/(1 + α)
✓β = α/(1 − α) and α = β/(1 + β). Check: α must come out less than 1, and β much greater than 1.
3
Taking the ripple frequency of a full-wave rectifier equal to the input frequency
✓A full-wave rectifier gives two pulses per cycle, so the ripple frequency is 2f (100 Hz on 50 Hz mains).
4
Saying a photodiode or Zener regulator is operated in forward bias
✓Both are operated in reverse bias. Only the LED among these devices is forward biased.
5
Forgetting the load current in Zener problems and taking I_Z = I_s
✓I_Z = I_s − I_L. Only with no load connected does the whole series current flow through the Zener.
6
Treating XOR as OR
✓For A = B = 1, OR gives 1 but XOR gives 0. XOR is 1 only when the inputs differ.

🎯 Practice Yourself

🎯Practice Yourself6 questions

Q1
A full-wave rectifier is fed from a 50 Hz supply. What is the frequency of the ripple in its output? What would it be for a half-wave rectifier?
Q2
The common-base current gain of a transistor is 0.96. Find its common-emitter current gain.
Q3
A transistor has β = 150. Find α.
Q4
An LED has a band gap of 1.9 eV. Estimate the wavelength of the light it emits. (h = 6.63×10⁻³⁴ J s, c = 3×10⁸ m/s, e = 1.6×10⁻¹⁹ C)
Q5
For inputs A = 1 and B = 0, write the outputs of the NAND, NOR and XOR gates.
Q6
A 6 V Zener regulator has a series resistance of 100 Ω and an input of 12 V. Find the Zener current (a) with no load, (b) with a 300 Ω load.

📝 Notes

Semiconductor Devices — Maharashtra HSC Overview

Chapter 16 of the Maharashtra Board Std XII Physics textbook uses the p-n junction from Std XI to build working devices: rectifiers, special-purpose diodes, the bipolar junction transistor and logic gates.

Diodes at work

Rectifiers: a single diode passes one half of each cycle (half-wave). Two diodes with a centre-tapped transformer, or a bridge of four, pass both halves (full-wave). Either way the output is pulsating DC. A capacitor filter smooths it.
Zener diode: heavily doped and operated in reverse breakdown. The voltage across it stays nearly constant at $V_Z$ , which makes it a voltage regulator. Use $I_s = (V_{in} - V_Z)/R_s$ and $I_Z = I_s - I_L$ .
Optoelectronic devices: a photodiode (reverse biased) and a solar cell (unbiased) turn light into current. An LED (forward biased) turns current into light. In each case the band gap sets the wavelength through $\lambda = hc/E_g$ .

The transistor

A BJT has a heavily doped emitter, a thin, lightly doped base and a larger collector. With the emitter–base junction forward biased and the collector–base junction reverse biased, most carriers from the emitter cross the thin base into the collector. So $I_C$ is nearly equal to $I_E$ ( $\alpha$ close to 1), while $I_B$ is small ( $\beta$ large). Every numerical uses $I_E = I_B + I_C$ together with $\beta = \alpha/(1-\alpha)$ .

Logic gates

Learn the truth tables of OR, AND, NOT, NAND, NOR and XOR. NAND and NOR are universal gates. For combination circuits, label the output of each intermediate gate, build the truth table column by column, and compare the final column with the truth tables of the basic gates.