Explanation

I_C = β × I_B

= 150 × 20 μA

= 150 × 20 × 10^(-6) A

= 3 × 10^(-3) A

= 3.0 mA

Explanation

P = η × ρ × g × Q × H

= 0.85 × 1000 × 9.81 × 500 × 120

= 500,355,000 W

≈ 500 MW

Explanation

Protected length = 80% of 250 km

= 0.8 × 250

= 200 km

Explanation

The measured impedance is within the relay’s set zone, indicating a fault inside the protected section.

The relay triggers immediately to isolate the fault.

Explanation

Z = (0.2 + j0.8 Ω/km) × 50 km

= (0.2 × 50) + j(0.8 × 50)

= 10 + j40 Ω

Explanation

Traveling wave protection detects faults almost instantly by sensing high-frequency waves generated at the fault location.

It is highly suitable for evolving or fast-developing faults in transmission lines.

Explanation

The condenser converts exhaust steam from the turbine into water, enabling efficient reuse in the boiler.

This improves the overall efficiency of the Rankine cycle and reduces water consumption.

Explanation

In FM, the carrier frequency varies in proportion to the message signal.

The amplitude remains constant, which improves noise immunity compared to AM.

Explanation

PID controllers combine proportional, integral, and derivative actions, improving both transient and steady-state responses.

Proportional reduces error, integral eliminates steady-state error, and derivative improves transient stability.

Explanation

Lyapunov’s method assesses stability of nonlinear systems without solving differential equations.

It determines if the system remains stable around an equilibrium point.