Question

6. The equation of an alternating current is i = 62.35 sin 323t A. Determine its (a) maximum value (b) frequency (c) r.m.s value (d) average value and (e) form fac​

Answer 1

Answer:

Correct option is

A

200Hz,50A

i=50  

2

sin(400πt)A

=i  

max

sin(wt)A

So, w=400π

2πf=400π

f=200Hz

i  

max

​

=50  

2

​

 

i  

rms

​

=  

2

​

 

i  

max

​

 

​

 

=  

2

​

 

50  

2

=50A

Explanation:

Answer 2

Answer:

(a) Maximum value of current, $I_{m} =62.35A$

(b) Frequency, $w=323$ rad/s

(c) R.M.S value of current, $I_{RMS}=44A$

(d) Average value of current, $I_{av}=39.72A$

(e) Form Factor,$F.F.=1.11$

Explanation:

A sinusoid is a signal waveform which has the form of cosine or sine function.

For most of the time, alternating current (ac) refers to a sinusoidal waveform. Sinusoid means the value has positive and negative values in specific interval.

An ac circuit is a circuit which is driven by ac current or voltage sources.

$I=I_{m} sinwt$

where,

$I_{m}$=maximum Current( amplitude of the sinusoid)

$w$ is angular frequency in radians/s

Root Mean Square Value: The RMS Value of an Alternating Current is that when it compare to the Direct Current, then both AC and DC current produce the same amount of heat when flowing through the same circuit for a specific time period.

$I_{RMS} =\frac{I_{m} }{\sqrt{2} }$

Average Value: If we convert the alternating current (AC) sine wave into direct current (DC) sine wave through rectifiers, then the converted value to the DC is known as the average value of that alternating current sine wave.

$I_{av}=0.637I_{m}$

Form Factor: the form factor of an alternating current waveform (signal) is the ratio of the RMS (root mean square) value to the average value (mathematical mean of absolute values of all points on the waveform).

$F.F=\frac{I_{RMS} }{I_{av} }$

Given: Equation of an alternating current

$i = 62.35 sin 323t$

So, comparing with $I=I_{m} sinwt$ we get

$I_{m} =62.35A$

$w=323$rad/s

(a) Maximum value of current, $I_{m} =62.35A$

(b) Frequency, $w=323$ rad/s

(c)  R.M.S value of current

$I_{RMS} =\frac{I_{m} }{\sqrt{2} }$

$=\frac{62.35}{\sqrt{2} }$A

$=44.088A\approx44A$

(d) Average value of current,

$I_{av}=0.637I_{m}$

$=0.637\times62.35\\=39.72A$

(e) Form factor,

​$F.F=\frac{I_{RMS} }{I_{av} }$

$=\frac{44}{39.72} \\=1.11$

#SPJ2