Question

The current and voltage in circuit is given by i=3.5sin(628t+30°) v=28sin(628t+30°)

Answer 1

Answer:

An alternating voltage e=200 sin 314t is applied to a device which offers an ohmic resistance of 20 ohm to the flow of current in one direction, while preventing the flow of current in opposite direction. Calculate rms value, average value and form factor for the current over one cycle.

Solution:

The instantaneous voltage applied to the rectifying device is given by the expression

e = 200 sin 314 t

Maximum value of applied voltage,

Emax = Coefficient of the sine of time angle = 200 volts

Resistance of rectifying device, R = 20 ohm

Maximum value of half-wave rectified alternating current,

I_{max} = \dfrac{E_{max}}{R} = \dfrac{200}{20} = 10\ amperes

RMS value of half-wave rectified alternating current,

I_{rms} = \dfrac{I_{max}}{2} = \dfrac{10}{2} = 5\ amperes Ans.

Average value of the half wave rectified alternating current,

I_{av} = \dfrac{I_{max}}{\pi} = \dfrac{10}{\pi} = 3.18\ amperes Ans.

Form factor of the half-wave rectified alternating current

= \dfrac{I_{rms}}{I_{av}} = \dfrac{5}{3.18} = 1.57 Ans.