Electrical Engineering (CBT-2)

Notes

• Series shares current, parallel shares voltage: Kirchhoff’s current law balances a node and his voltage law closes a loop. On AC the same element also has reactance, X_{L} = 2\pi f L or X_{C} = 1/(2\pi f C), so the source sees an impedance Z = \sqrt{R^2 + X^2}; power factor is R/Z and never X/Z, and series resonance is the frequency where X_{L} = X_{C} and the current peaks.
• Four machines, four jobs: A transformer stays electrical on both sides, V_{1}/V_{2} = N_{1}/N_{2} = I_{2}/I_{1}, and makes no shaft torque. A DC machine uses a commutator, and the series motor’s large starting torque is why it was the traction choice. An induction motor’s rotor has no supply leads and must run below N_{s} = 120f/P, because zero slip would mean no rotor current.
• The power system raises voltage to cut current: Three-phase line current is I = P/(\sqrt{3} V \cos\phi), so raising the transmission voltage lowers the current and the I^2 R loss without changing the power being sent. Protection is a decision plus an interruption - the relay decides that a fault is present and the breaker opens the circuit, while a CT or PT only scales the line quantity down.
• Which instrument reads what: A permanent-magnet moving-coil meter reads a DC average and reads zero on AC, while a moving-iron meter reads RMS on either. A dynamometer wattmeter reads power, an induction meter integrates that power into kilowatt-hours, and a megger injects a high DC voltage to read insulation resistance rather than continuity.
• Utilization is the end use: Illumination on a surface follows the inverse square, E = I \cos\theta / d^2 lux, so doubling the mounting height leaves a quarter of the lux. Resistance heating is I^2 R, while induction and dielectric heating put the energy inside the work; arc welding wants a high current at low voltage, and traction wants a large starting torque.
• Panel electronics: A silicon diode conducts one way past about 0.7 V. A half-wave rectifier averages V_{m}/\pi and a full-wave bridge 2V_{m}/\pi, and a shunt capacitor after it cuts ripple rather than changing that average. A transistor is a switch at cut-off or saturation and an amplifier in the active region, an inverting op-amp has gain -R_{f}/R_{in}, and a Zener works in reverse breakdown as a reference.

Formulas

• AC single element: X_{L} = 2\pi f L, X_{C} = 1/(2\pi f C), Z = \sqrt{R^2 + X^2}, power factor = R/Z. Series resonance is where X_{L} = X_{C} and current peaks.
• Transformer: V_{1}/V_{2} = N_{1}/N_{2} = I_{2}/I_{1}, electrical on both sides, no shaft torque.
• Induction motor synchronous speed N_{s} = 120f/P; slip must be non-zero or there is no rotor current. Slip s = (N_{s} - N)/N_{s}.
• Three-phase line current I = P/(\sqrt{3} V \cos\phi), so raising transmission voltage lowers current and the I^2 R loss for the same power.
• Instrument to quantity: PMMC reads a DC average (zero on AC), moving iron reads RMS on either, dynamometer reads power, induction meter integrates kWh, megger reads insulation resistance.
• Utilization: illumination E = I \cos\theta / d^2 lux, resistance heating = I^2 R, half-wave rectifier average V_{m}/\pi, full-wave bridge 2V_{m}/\pi, inverting op-amp gain -R_{f}/R_{in}.

Exam traps & shortcuts

• Power factor is R/Z, never X/Z. Sketch the impedance triangle if the option set offers both.
• A transformer changes voltage and current but produces no shaft torque — it is not a machine that can drive a load.
• An induction motor cannot reach synchronous speed: zero slip means zero rotor current and zero torque.
• Raising transmission voltage cuts the current and the I^2 R loss without changing the power delivered.
• A PMMC meter reads zero on AC. A relay decides; only the breaker interrupts, and a CT or PT merely scales.
• Doubling the mounting height leaves a quarter of the lux — illumination follows the inverse square, not the inverse.

Reference tables