Part II — Basic Electrical Engineering

Chapter 2: Circuit Fundamentals

2.1 Ohm's Law

Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across those points, provided temperature and other physical conditions remain constant: V = IR, where R is resistance in ohms (Ω). Resistance of a conductor is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area — resistance increases with length and decreases with cross-sectional area.

2.2 Kirchhoff's Laws

Kirchhoff's Current Law (KCL) states that the algebraic sum of currents entering and leaving a node (junction) is zero (total current into a node equals total current out) — a direct consequence of conservation of charge. Kirchhoff's Voltage Law (KVL) states that the algebraic sum of all voltages around any closed loop in a circuit is zero — a direct consequence of conservation of energy.

2.3 Series and Parallel Circuits

In a series circuit, the same current flows through all components, and total resistance is the sum of individual resistances: R_total = R1 + R2 + ... + Rn. In a parallel circuit, voltage across all branches is the same, and total resistance is given by 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn — for two resistors in parallel, this simplifies to R_total = (R1×R2)/(R1+R2), which is always less than the smallest individual resistance.

2.4 Network Theorems

Thevenin's Theorem states that any linear two-terminal network can be replaced by an equivalent circuit consisting of a single voltage source (Thevenin voltage, Vth) in series with a single resistance (Thevenin resistance, Rth). Norton's Theorem is the dual of Thevenin's theorem, representing the network as a current source in parallel with a resistance. The Superposition Theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) in any element equals the algebraic sum of the responses caused by each source acting alone (with all other independent sources set to zero — voltage sources short-circuited, current sources open-circuited). Maximum Power Transfer Theorem states that maximum power is transferred from a source to a load when the load resistance equals the source's (Thevenin) internal resistance.

2.5 AC Fundamentals

An alternating current (AC) periodically reverses direction, typically following a sinusoidal waveform, characterised by frequency (f, in Hz), amplitude, and phase. RMS (Root Mean Square) value of a sinusoidal AC quantity is the equivalent DC value that would produce the same heating effect; for a pure sine wave, RMS = Peak value / √2 ≈ 0.707 × Peak value. Average value of a sinusoidal AC quantity over a half cycle is Average = 2/π × Peak value ≈ 0.637 × Peak value. The Form Factor (RMS/Average) for a pure sine wave is approximately 1.11, and the Peak Factor (Peak/RMS) is approximately 1.414. Standard AC supply frequency in India is 50 Hz.

2.6 Practice Set — Circuit Fundamentals (16 MCQs)

1. Ohm's Law states that, at constant temperature:
   (a) V = I/R (b) V = IR (c) V = I + R (d) V = I²R only
2. Resistance of a conductor (R = ρL/A) increases with:
   (a) Increasing length (b) Increasing cross-sectional area (c) Decreasing length (d) Decreasing resistivity
3. Kirchhoff's Current Law (KCL) is a direct consequence of conservation of:
   (a) Energy (b) Charge (c) Momentum (d) Mass alone
4. Kirchhoff's Voltage Law (KVL) is a direct consequence of conservation of:
   (a) Charge (b) Energy (c) Momentum (d) Mass
5. In a series circuit, total resistance is:
   (a) The sum of individual resistances (b) The reciprocal of the sum of reciprocals (c) Always less than the smallest resistance (d) Always zero
6. In a parallel circuit, the voltage across all branches is:
   (a) Different for each branch (b) The same across all branches (c) Zero (d) Equal to the source current
7. For two resistors R1 and R2 in parallel, the equivalent resistance is:
   (a) R1 + R2 (b) (R1×R2)/(R1+R2) (c) R1 − R2 (d) √(R1×R2)
8. Thevenin's Theorem replaces a linear two-terminal network with:
   (a) A current source in parallel with a resistance (b) A voltage source in series with a resistance (c) Two voltage sources in parallel (d) A pure resistance only
9. Norton's Theorem represents a network as:
   (a) A voltage source in series with a resistance (b) A current source in parallel with a resistance (c) A pure inductor (d) A pure capacitor
10. The Superposition Theorem is applicable to:
    (a) Only non-linear circuits (b) Linear circuits with multiple independent sources (c) Only single-source circuits (d) Only DC circuits with no sources
11. Maximum power transfer to a load occurs when load resistance equals:
    (a) Zero (b) Infinity (c) The source's Thevenin resistance (d) Twice the source resistance
12. For a pure sine wave, the RMS value is related to the peak value by:
    (a) RMS = Peak × 2 (b) RMS = Peak / √2 (c) RMS = Peak × π (d) RMS = Peak / 2
13. For a pure sine wave, the average value over a half cycle is approximately:
    (a) 0.5 × Peak (b) 0.637 × Peak (c) 0.707 × Peak (d) 1.11 × Peak
14. The Form Factor (RMS/Average) for a pure sine wave is approximately:
    (a) 0.707 (b) 1.0 (c) 1.11 (d) 1.414
15. The Peak Factor (Peak/RMS) for a pure sine wave is approximately:
    (a) 0.707 (b) 1.0 (c) 1.11 (d) 1.414
16. The standard AC supply frequency in India is:
    (a) 25 Hz (b) 50 Hz (c) 60 Hz (d) 100 Hz

Answer Key

1.(b)

2.(a)

3.(b)

4.(b)

5.(a)

6.(b)

7.(b)

8.(b)

9.(b)

10.(b)

11.(c)

12.(b)

13.(b)

14.(c)

15.(d) 16.(b)