Quick-Revision Formula & Fact Capsules

This chapter condenses the most frequently tested formulas and one-line facts for last-minute revision.

7A.1 Circuit Fundamentals

Ohm's Law: V = IR. Series resistance: R = R1+R2+.... Parallel resistance (two): R = R1R2/(R1+R2). RMS (sine wave): 0.707 × Peak. Average (sine wave, half cycle): 0.637 × Peak. Form Factor: ~1.11. Peak Factor: ~1.414. Indian AC supply frequency: 50 Hz.

7A.2 Machines

Transformer ratio: V2/V1 = N2/N1 = I1/I2. Max transformer efficiency: copper loss = iron loss. Induction motor slip: s = (Ns−Nr)/Ns. Synchronous speed: Ns = 120f/P. Synchronous machines: zero slip. Induction motor: always some positive slip (Nr < Ns).

7A.3 Power Systems

Common Indian transmission voltages: 220 kV, 400 kV, 765 kV. Typical LV consumer supply: 230V (1-phase) / 400V (3-phase). Power factor: cos φ. PF improvement device: capacitor banks.

7A.4 Measurements

Ammeter: series, near-zero resistance. Voltmeter: parallel, very high resistance. PMMC: DC only. Moving Iron: AC and DC. Megger test voltage: 500V/1000V typical.

7A.5 Electronics

Silicon diode forward drop: ~0.7V. Germanium diode forward drop: ~0.3V. BJT terminals: Emitter, Base, Collector. Current gain: β = Ic/Ib.

7A.6 Exam Pattern

RRB JE negative marking: 1/3 mark. CBT 2 Technical Abilities: ~100 marks.

7A.7 Practice Set — Formula Capsules (14 MCQs)

1. Ohm's Law is expressed as:
   (a) V = IR (b) V = I/R (c) V = I+R (d) V = I²R only
2. For a pure sine wave, RMS value is approximately:
   (a) 0.5 × Peak (b) 0.637 × Peak (c) 0.707 × Peak (d) 1.11 × Peak
3. Synchronous speed formula is:
   (a) Ns = 120f/P (b) Ns = f/120P (c) Ns = P/120f (d) Ns = 120P/f
4. Maximum transformer efficiency occurs when:
   (a) Copper loss = 0 (b) Iron loss = 0 (c) Copper loss = Iron loss (d) Copper loss = 2× Iron loss
5. Standard AC supply frequency in India is:
   (a) 25 Hz (b) 50 Hz (c) 60 Hz (d) 100 Hz
6. Silicon diode forward-bias threshold voltage is approximately:
   (a) 0.1V (b) 0.3V (c) 0.7V (d) 5V
7. A BJT's current gain (β) is defined as:
   (a) Ib/Ic (b) Ic/Ib (c) Ic×Ib (d) Ic+Ib
8. An ideal ammeter has:
   (a) Very high resistance (b) Near-zero resistance (c) Infinite resistance (d) Negative resistance
9. An ideal voltmeter has:
   (a) Near-zero resistance (b) Very high resistance (c) Resistance equal to load (d) Negative resistance
10. A common extra-high transmission voltage level in India is:
    (a) 33 kV (b) 11 kV (c) 765 kV (d) 230V
11. RRB JE examinations apply negative marking of:
    (a) 1/4 mark (b) 1/3 mark (c) 1/2 mark (d) None
12. A Megger typically applies a test voltage of approximately:
    (a) 5V (b) 12V (c) 500V or 1000V (d) 50,000V
13. Induction motor slip is defined as:
    (a) (Ns+Nr)/Ns (b) (Ns−Nr)/Ns (c) Ns/Nr (d) Nr/Ns
14. For two resistors in parallel, equivalent resistance is:
    (a) R1+R2 (b) (R1×R2)/(R1+R2) (c) R1−R2 (d) √(R1×R2)

Answer Key

1.(a)

2.(c)

3.(a)

4.(c)

5.(b)

6.(c)

7.(b)

8.(b)

9.(b)

10.(c)

11.(b)

12.(c)

13.(b) 14.(b)