Alternating Current

Notes

1. Electric Current

The flow of electric charge or electrons through a wire is called electric current.

2. Types of Electric Current

1. Direct Current (D.C.)
2. Alternating Current (A.C.)

Direct Current (D.C.)

The current whose direction does not change with time through a load is known as direct current (D.C.).

For D.C.:

I = Q/t

Also:

I = ne/t

and:

I = neAv_d

Alternating Current (A.C.)

The current whose direction changes periodically through a load is known as alternating current (A.C.).

The alternating current can be represented as:

I = I₀ sin(ωt + φ)

Similarly, alternating voltage can be represented as:

V = V₀ sin(ωt + φ)

or:

V = ε = ε₀ sin(ωt + φ)

The current that varies like a sinusoidal wave or function is called alternating current.

Terms Used in Alternating Current

• I: Instantaneous current of A.C.
• I₀: Maximum value of A.C.
• ωt + φ: Phase at time t
• φ: Initial phase or phase constant
• ω = 2πf: Angular frequency
• t: Time period
• f = 1/T: Frequency
• A: Area
• B: Magnetic field

For a coil rotating in a uniform magnetic field:

I₀ = NABω

3. Time Period

The time taken to complete one cycle is called the time period.

T = 2π/ω

Also:

T = 1/f

Here, 2π is the angular displacement in one cycle.

4. Frequency

The number of cycles completed per second is called frequency.

f = Number of cycles / Time period

f = 1/T

Also:

ω = 2πf

For India:

f = 50 Hz = 50 cps

Therefore:

ω = 2π × 50 = 314 rad/s

For U.S.:

f = 60 Hz

5. Peak or Maximum Value / Amplitude

The maximum value of A.C. is called its peak value or amplitude.

It is denoted by:

I₀ for current.

V₀ for voltage.

For the rotating coil:

I₀ = NABω

The peak value may be in either direction, i.e. positive or negative.

6. Phase

Phase is a physical quantity.

It represents the instantaneous value and direction.

It is a dimensionless quantity.

Its SI unit is radian (rad).

7. Phase Difference

The difference between the phase of current and the phase of voltage is known as phase difference.

Let:

V = V₀ sin(ωt + φ₁)

and:

I = I₀ sin(ωt + φ₂)

Therefore:

Phase difference, φ = φ₂ − φ₁

8. Important Points of A.C.