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Computer Science and Electronics for Digital Assistant · Chapter 8

Circuit Theory and Electronic Devices

What to remember

  • Ohm's law and Kirchhoff's laws solve most circuits. V = I × R; the current sum at a node is zero; the voltage sum around a loop is zero.
  • Semiconductors (silicon, germanium) make diodes and transistors. A diode passes current one way; a transistor amplifies or switches.
  • Logic gates build digital circuits. AND, OR, NOT, NAND, NOR, XOR and XNOR work on binary 0 and 1.

Basic quantities and units

QuantitySymbolUnitMeaning
ChargeQcoulomb (C)Amount of electric charge
CurrentIampere (A)Rate of flow of charge, I = Q / t
VoltageVvolt (V)Potential difference, work per unit charge
ResistanceRohm (Ω)Opposition to current
PowerPwatt (W)P = V × I = I²R = V²/R
EnergyEjoule (J) or kWhE = P × t
CapacitanceCfarad (F)Ability to store charge, Q = C × V
InductanceLhenry (H)Opposition to change of current
Frequencyfhertz (Hz)Cycles per second

One kilowatt-hour (1 kWh) is the "unit" of electricity billed. A 1000 W heater used for 1 hour consumes 1 kWh.

Ohm's law and resistors

Ohm's law: at constant temperature, V = I R. Resistance of a wire: R = ρ L / A, where ρ is resistivity, L is length and A is area of cross section. A longer or thinner wire has more resistance. Conductors such as copper and silver have low resistivity. Insulators such as rubber and glass have very high resistivity. In metals, resistance rises with temperature.

Series connection: the same current flows through all. R_total = R1 + R2 + R3. Voltages add.

Parallel connection: the same voltage is across all. 1/R_total = 1/R1 + 1/R2 + 1/R3. Currents add. For two resistors, R = (R1 × R2)/(R1 + R2).

Worked example: 6 Ω and 3 Ω in parallel give (6 × 3)/(6 + 3) = 2 Ω. In series they give 9 Ω.

Worked example: a 12 V battery across 4 Ω gives I = 12/4 = 3 A, and power = 12 × 3 = 36 W.

Resistor colour code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9. The first two bands give digits, the third gives the multiplier, the fourth gives tolerance (gold ±5%, silver ±10%).

Network laws

  • Kirchhoff's Current Law (KCL): the algebraic sum of currents at a junction is zero. Current in equals current out.
  • Kirchhoff's Voltage Law (KVL): the algebraic sum of voltages around a closed loop is zero.
  • Voltage divider: in a series pair, V across R1 = V × R1/(R1 + R2).
  • Current divider: in a parallel pair, current in R1 = I × R2/(R1 + R2).
  • Superposition theorem: in a linear circuit with many sources, the response is the sum of responses of each source acting alone.
  • Thevenin's theorem: any linear network seen from two terminals is a single voltage source Vth in series with a resistance Rth.
  • Norton's theorem: the same network is a current source in parallel with a resistance.
  • Maximum power transfer: a source gives maximum power to the load when load resistance equals the source resistance.

AC basics, capacitors and inductors

Alternating current changes direction and magnitude with time. For a sine wave, the RMS value = peak value / √2, which is about 0.707 × peak. Frequency f = 1/T, where T is the time period. Mains supply in India is 50 Hz, so T = 20 ms. Mains 230 V is an RMS value.

ElementOppositionPhase between voltage and current
ResistorRIn phase
InductorX_L = 2πfLCurrent lags voltage by 90°
CapacitorX_C = 1/(2πfC)Current leads voltage by 90°

Series RLC impedance: Z = √(R² + (X_L − X_C)²). Resonance occurs when X_L = X_C, and the resonant frequency is f₀ = 1/(2π√(LC)). At series resonance, impedance is minimum (equal to R) and current is maximum. Power factor = cos φ = R/Z. Capacitors in parallel add: C = C1 + C2. Capacitors in series: 1/C = 1/C1 + 1/C2. Time constant of an RC circuit is τ = R × C; of an RL circuit is τ = L/R.

Semiconductors and diodes

Pure silicon and germanium are intrinsic semiconductors. Adding a small amount of impurity (doping) makes them extrinsic. N-type has a pentavalent impurity (phosphorus, arsenic) and electrons are the majority carriers. P-type has a trivalent impurity (boron, gallium) and holes are the majority carriers. Silicon has a band gap of about 1.1 eV and germanium about 0.7 eV. Temperature increases conductivity of semiconductors, unlike metals.

A P-N junction diode passes current in forward bias and blocks it in reverse bias. Knee (cut-in) voltage is about 0.7 V for silicon and 0.3 V for germanium. Uses:

  • Rectifier: converts AC to DC. A half-wave rectifier uses one diode; a full-wave rectifier uses two diodes with a centre-tap transformer or four diodes in a bridge.
  • Zener diode: works in reverse breakdown and is used as a voltage regulator.
  • LED: emits light when forward biased.
  • Photodiode: works in reverse bias and senses light.

Ripple is the AC left in the DC output; a capacitor filter reduces it. For a full-wave rectifier, ripple frequency is twice the input frequency (100 Hz for 50 Hz mains). Average DC output of a half-wave rectifier is Vm/π and of a full-wave rectifier is 2Vm/π.

Transistors and amplifiers

A bipolar junction transistor (BJT) has three terminals: emitter, base and collector. Types are NPN and PNP. Relations: I_E = I_B + I_C. Current gain β = I_C / I_B. For example, if I_B = 20 µA and β = 100, I_C = 2 mA.

The transistor works as a switch (cut-off and saturation) and as an amplifier (active region). In the active region, the emitter-base junction is forward biased and the collector-base junction is reverse biased. Configurations are common emitter (high gain, most used), common base, and common collector (emitter follower, used for matching). A field effect transistor (FET) or MOSFET is voltage controlled and has very high input impedance. An operational amplifier (op-amp) has very high gain and high input impedance. Inverting amplifier gain = −Rf/Rin. Non-inverting gain = 1 + Rf/Rin.

An oscillator makes an AC signal without an input signal. A 555 timer IC works as a timer and a pulse generator.

Digital electronics

Number systems: binary (base 2), octal (8), decimal (10), hexadecimal (16). Example: binary 1011 = 8 + 2 + 1 = 11 in decimal. Decimal 13 = binary 1101. Hex digits run 0 to 9 and A to F; hex F = 15.

GateOutput is 1 when
ANDAll inputs are 1
ORAt least one input is 1
NOTInput is 0 (it inverts)
NANDNot all inputs are 1 (AND inverted)
NORAll inputs are 0 (OR inverted)
XORThe inputs are different
XNORThe inputs are the same

NAND and NOR are called universal gates because any gate can be built from them. De Morgan's laws: (A·B)' = A' + B' and (A + B)' = A'·B'. A half adder adds two bits (sum = A XOR B, carry = A AND B). A full adder adds three bits. A flip-flop stores one bit and is the basic memory element. A multiplexer selects one of many inputs. A decoder converts a binary code to one of many outputs. A counter counts clock pulses.

Exam traps

  • Series and parallel: series adds resistances; parallel adds conductances.
  • Peak and RMS: RMS = peak/√2, not peak/2.
  • Inductor and capacitor: in an inductor current lags; in a capacitor current leads (ICE: current leads in a capacitor).
  • N-type and P-type: N-type majority carriers are electrons; P-type are holes. The material itself is neutral.
  • Forward and reverse bias: current flows in forward bias only (apart from tiny leakage).
  • Zener and ordinary diode: the Zener is used in reverse breakdown for regulation.
  • NAND and NOR: both are universal; NAND is AND followed by NOT.
  • XOR and XNOR: XOR gives 1 for different inputs, XNOR gives 1 for same inputs.
  • Half-wave and full-wave ripple: full-wave ripple frequency is double.
  • Power and energy: watt is power; kWh is energy.

One-liners

  • 1. Unit of resistance is the ohm.
  • 2. Parallel resistors always give a total lower than the smallest one.
  • 3. KCL is based on conservation of charge.
  • 4. KVL is based on conservation of energy.
  • 5. Mains frequency in India is 50 Hz.
  • 6. Silicon knee voltage is about 0.7 V.
  • 7. A bridge rectifier uses four diodes.
  • 8. A Zener diode regulates voltage.
  • 9. In a transistor, I_E = I_B + I_C.
  • 10. NAND and NOR are universal gates.
  • 11. Binary 1010 equals decimal 10.
  • 12. At resonance in a series RLC circuit, impedance is minimum.

Practice questions

  1. A 12 V battery is connected across a 4 ohm resistor. The current is

    1. 4 A
    2. 2 A
    3. 48 A
    4. 3 A
    Answer

    D. 3 A

    I = V/R = 12/4 = 3 A.

  2. Resistors of 6 ohm and 3 ohm are connected in parallel. The equivalent resistance is

    1. 18 ohm
    2. 9 ohm
    3. 4.5 ohm
    4. 2 ohm
    Answer

    D. 2 ohm

    (6 x 3)/(6 + 3) = 18/9 = 2 ohm.

  3. Resistors of 10, 20 and 30 ohm are connected in series. The total resistance is

    1. 60 ohm
    2. 600 ohm
    3. 5.45 ohm
    4. 6 ohm
    Answer

    A. 60 ohm

    Series resistances add: 10 + 20 + 30 = 60 ohm.

  4. A 100 W lamp burns for 10 hours. The energy used is

    1. 100 kWh
    2. 0.1 kWh
    3. 1 kWh
    4. 10 kWh
    Answer

    C. 1 kWh

    100 W x 10 h = 1000 Wh = 1 kWh.

  5. A 2 kW heater runs for 5 hours. The number of units consumed is

    1. 7
    2. 25
    3. 2.5
    4. 10
    Answer

    D. 10

    2 kW x 5 h = 10 kWh = 10 units.

  6. A 12 V supply is across a series pair of 2 kilo-ohm and 4 kilo-ohm resistors. The voltage across the 4 kilo-ohm resistor is

    1. 4 V
    2. 6 V
    3. 8 V
    4. 10 V
    Answer

    C. 8 V

    V = 12 x 4/(2 + 4) = 8 V.

  7. A sine wave has a peak value of 141.4 V. Its RMS value is about

    1. 100 V
    2. 282.8 V
    3. 70.7 V
    4. 200 V
    Answer

    A. 100 V

    RMS = peak/1.414 = 100 V.

  8. The mains frequency is 50 Hz. The time period of one cycle is

    1. 0.2 s
    2. 50 ms
    3. 2 ms
    4. 20 ms
    Answer

    D. 20 ms

    T = 1/f = 1/50 = 0.02 s = 20 ms.

  9. In a series circuit R = 3 ohm, X_L = 10 ohm and X_C = 6 ohm. The impedance is

    1. 7 ohm
    2. 19 ohm
    3. 13 ohm
    4. 5 ohm
    Answer

    D. 5 ohm

    Z = sqrt(3^2 + (10 - 6)^2) = sqrt(25) = 5 ohm.

  10. In an AC circuit R = 6 ohm and Z = 10 ohm. The power factor is

    1. 0.8
    2. 1.67
    3. 0.6
    4. 0.4
    Answer

    C. 0.6

    Power factor = R/Z = 6/10 = 0.6.

  11. A transistor has base current 20 microamp and current gain 100. The collector current is

    1. 2 mA
    2. 0.5 mA
    3. 0.2 mA
    4. 20 mA
    Answer

    A. 2 mA

    I_C = beta x I_B = 100 x 20 microamp = 2 mA.

  12. A transistor has I_B = 0.1 mA and I_C = 9.9 mA. The emitter current is

    1. 9.8 mA
    2. 99 mA
    3. 10 mA
    4. 10.9 mA
    Answer

    C. 10 mA

    I_E = I_B + I_C = 0.1 + 9.9 = 10 mA.

  13. The decimal value of the binary number 1011 is

    1. 11
    2. 9
    3. 13
    4. 15
    Answer

    A. 11

    8 + 0 + 2 + 1 = 11.

  14. The binary form of decimal 13 is

    1. 1110
    2. 1011
    3. 1001
    4. 1101
    Answer

    D. 1101

    13 = 8 + 4 + 1 = 1101.

  15. Capacitors of 3 microfarad and 6 microfarad are connected in series. The equivalent capacitance is

    1. 2 microfarad
    2. 4.5 microfarad
    3. 18 microfarad
    4. 9 microfarad
    Answer

    A. 2 microfarad

    (3 x 6)/(3 + 6) = 2 microfarad.

  16. An inverting op-amp has Rf = 100 kilo-ohm and Rin = 10 kilo-ohm. The voltage gain is

    1. -1
    2. -10
    3. +10
    4. +11
    Answer

    B. -10

    Gain = -Rf/Rin = -100/10 = -10.

  17. A full-wave rectifier works on 50 Hz mains. The ripple frequency is

    1. 200 Hz
    2. 25 Hz
    3. 100 Hz
    4. 50 Hz
    Answer

    C. 100 Hz

    Full-wave rectification doubles the frequency: 2 x 50 = 100 Hz.

  18. A 10 V supply is across a 20 ohm resistor. The power dissipated is

    1. 0.5 W
    2. 200 W
    3. 2 W
    4. 5 W
    Answer

    D. 5 W

    P = V^2/R = 100/20 = 5 W.

  19. If the length of a wire is doubled with the same area and material, its resistance

    1. becomes four times
    2. stays the same
    3. is halved
    4. doubles
    Answer

    D. doubles

    R = rho L/A, so R is proportional to L.

  20. Which law states that the sum of currents at a junction is zero?

    1. Kirchhoff's current law
    2. Faraday's law
    3. Kirchhoff's voltage law
    4. Ohm's law
    Answer

    A. Kirchhoff's current law

    KCL is based on conservation of charge.

  21. Kirchhoff's voltage law is based on conservation of

    1. mass
    2. energy
    3. momentum
    4. charge
    Answer

    B. energy

    The voltage sum around a loop is zero because energy is conserved.

  22. Which theorem replaces a linear network by a voltage source in series with a resistance?

    1. Norton's theorem
    2. Millman's rule
    3. Thevenin's theorem
    4. Superposition theorem
    Answer

    C. Thevenin's theorem

    Thevenin gives Vth in series with Rth; Norton gives a current source in parallel.

  23. Maximum power is transferred to a load when the load resistance is

    1. equal to the source resistance
    2. zero
    3. infinite
    4. twice the source resistance
    Answer

    A. equal to the source resistance

    This is the maximum power transfer theorem.

  24. In a pure capacitor, the current

    1. lags the voltage by 90 degrees
    2. is in phase with the voltage
    3. leads the voltage by 90 degrees
    4. is zero always
    Answer

    C. leads the voltage by 90 degrees

    For a capacitor, current leads voltage by 90 degrees.

  25. An N-type semiconductor is made by doping silicon with

    1. a trivalent impurity such as boron
    2. a noble gas
    3. a heavier metal such as copper
    4. a pentavalent impurity such as phosphorus
    Answer

    D. a pentavalent impurity such as phosphorus

    Pentavalent donors give extra electrons.

  26. The majority carriers in a P-type semiconductor are

    1. neutrons
    2. holes
    3. electrons
    4. protons
    Answer

    B. holes

    P-type material has holes as majority carriers.

  27. The approximate knee voltage of a silicon diode is

    1. 0.3 V
    2. 1.5 V
    3. 5 V
    4. 0.7 V
    Answer

    D. 0.7 V

    Silicon conducts after about 0.7 V; germanium about 0.3 V.

  28. Which diode is used as a voltage regulator in reverse breakdown?

    1. LED
    2. Varactor diode
    3. Zener diode
    4. Photodiode
    Answer

    C. Zener diode

    A Zener diode holds a constant voltage in breakdown.

  29. Which logic gate gives output 1 only when all inputs are 1?

    1. OR
    2. AND
    3. XOR
    4. NOR
    Answer

    B. AND

    AND needs all inputs high.

  30. Which gates are called universal gates?

    1. NAND and NOR
    2. NOT and AND
    3. XOR and XNOR
    4. AND and OR
    Answer

    A. NAND and NOR

    Any logic function can be built from NAND alone or NOR alone.

  31. Which gate gives output 1 when its two inputs are different?

    1. XOR
    2. NAND
    3. NOR
    4. XNOR
    Answer

    A. XOR

    XOR is 1 for unequal inputs.

  32. The sum output of a half adder is given by

    1. A AND B
    2. A OR B
    3. A NAND B
    4. A XOR B
    Answer

    D. A XOR B

    Sum = A XOR B and carry = A AND B.

  33. Statement 1: In a series circuit the same current flows through all resistors. Statement 2: In a parallel circuit the same voltage is across all branches. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

  34. Statement 1: Resistance of metals falls as temperature rises. Statement 2: Conductivity of semiconductors rises as temperature rises. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    Metal resistance rises with temperature; semiconductor conductivity increases.

  35. Statement 1: RMS value of a sine wave equals peak value divided by square root of 2. Statement 2: Mains 230 V is an RMS value. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

  36. Statement 1: In an inductor, current lags the voltage by 90 degrees. Statement 2: In a resistor, current and voltage are 90 degrees out of phase. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    A resistor has voltage and current in phase.

  37. Statement 1: A bridge rectifier uses four diodes. Statement 2: A half-wave rectifier gives output on both half cycles. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    A half-wave rectifier uses only one half cycle.

  38. Statement 1: At series resonance, X_L equals X_C. Statement 2: At series resonance, the impedance is maximum. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Impedance is minimum (equal to R) at series resonance.

  39. Statement 1: In the active region of a transistor, the emitter-base junction is forward biased. Statement 2: In the active region, the collector-base junction is forward biased. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    The collector-base junction is reverse biased in the active region.

  40. Statement 1: NOR gives 1 only when all inputs are 0. Statement 2: NAND is an AND gate followed by NOT. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

  41. Statement 1: A photodiode is operated in reverse bias. Statement 2: An LED emits light when forward biased. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

  42. Statement 1: Zener diodes are normally used in forward bias for regulation. Statement 2: Capacitors reduce ripple at a rectifier output. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    A Zener regulates in reverse breakdown; a filter capacitor smooths ripple.

  43. Statement 1: A kilowatt-hour is a unit of power. Statement 2: A watt is a unit of power. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    kWh is energy; watt is power.

  44. Statement 1: According to De Morgan's law, (A + B)' = A'.B'. Statement 2: According to De Morgan's law, (A.B)' = A'.B'. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    (A.B)' = A' + B'.

  45. Statement 1: The first two colour bands of a resistor give digits. Statement 2: The third band gives the multiplier. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

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