Question

What is alternating current? How alternating e.m.f. and current is represented mathematically. What do you mean by time period, frequency and amplitude of alternating current?

Answer 1

Alternating current

The current in which both the magnitude and direction undergo a complete cycle of changes periodically is called alternating current. It increases from zero to a maximum value, then decreases to zero and reverses in direction. It once again becomes maximum in this direction and then reduced to zero. This complete set of variations in magnitude and direction of current or e.m.f. is called a cycle. During one cycle, the current flows in one direction, of course, changing in magnitude in the first half cycle and in the opposite direction during the next half cycle.

Thus current whose magnitude changes with time and direction reverses periodically is called alternating current.

The instantaneous value of a.c. is given by

I = I₀ sin ωt Fig. ............. (I)

or I = I₀ cos ωt Fig. .............(II)

where I₀ is the peak value of a.c.

Similarly, the e.m.f. whose magnitude changes with time and direction reverses periodically is called alternating e.m.f.

The instantaneous alternating e.m.f. is given by

E = E₀ sin ωt ............ (III)

or E = E₀ cos ωt ........... (IV)

where ω = \(\frac{2\pi}{T}\)  is angular frequency.

Time period (T)

Time period is the time taken to complete one cycle.

Frequency (v)

Frequency is the number of cycles per second.

Amplitude (I₀). Amplitude of alternating current is the peak value of alternating current and is denoted by I₀.