Explanation

Q = ∫[1,2] i dt = ∫[1,2] (3t² - t) dt

= [t³ - t²/2] from 1 to 2

= (2³ - 2²/2) - (1³ - 1²/2)

= (8 - 2) - (1 - 0.5)

= 6 - 0.5

= 5.5 C

Explanation

Capacitors supply reactive power to the circuit, which is considered positive in standard convention.

This helps improve power factor by compensating for inductive loads.

Explanation

Capacitance is maximum when the overlapping area between movable and fixed plates is greatest.

In a variable air capacitor, this occurs when the plates are fully aligned or exactly meshed.

Explanation

Modern synchronous generators typically generate voltage in the range of 13 kV to 30 kV at the generator terminals.

Step-up transformers are then used to transmit this voltage efficiently over long distances.

Explanation

Capacitance is directly proportional to plate area (A) and dielectric permittivity (ε), and inversely proportional to plate separation (d).

This formula is fundamental for designing parallel-plate capacitors.

Explanation

An op-amp integrator produces an output voltage proportional to the time integral of the input signal.

It is widely used in analog computation, waveform generation, and signal processing.

Explanation

If ω = 4 rad/s:

XL = j(4)(0.5)

= j2 Ω

Explanation

Rating: 50 Ah, 10 h discharge → Rated current = 50 Ah / 10 h = 5 A

Since asked current = 5 A (matches rated),

Time = Capacity / Current = 50 Ah / 5 A = 10 h

Explanation

f = cycles / time

= 100 cycles / 0.1 s

= 1000 Hz

= 1 kHz

Explanation

Pakistan’s first HVDC transmission line (Matiari‑Lahore ±660 kV) is designed to transmit up to 4,000 MW of power. 

This high‑capacity link helps evacuate bulk generation from the south to load centers in the north efficiently.