Question

The current in an ac circuit is given by i = (3 + 4sin1007t + 4cos100nt)A. The r.m.s. value of current will be​

Answer 1

Explanation:

Current is given as i=I

o

+I

1

sinwt

Rms current is given by I

rms

=

T

∫

o

T

i

2

dt

∴ I

rms

=

T

∫

o

T

(I

o

2

+I

1

2

sin

2

wt+2I

o

I

1

sinwt)dt

Or I

rms

=

I

o

2

T

∫

o

T

dt

+I

1

2

T

∫

o

T

sin

2

wtdt

+2I

o

I

1

T

∫

o

T

sinwtdt

Using

T

∫

o

T

sin

2

wt

=0.5 and

T

∫

o

T

sinwt

=0

We get I

rms

=

I

o

2

T

T

+I

1

2

×0.5+2I

o

I

1

×0

⟹ I

rms

=

I

o

2

+0.5I

1

2

Given : I

o

=3 I

1

=4

⟹ I

rms

=

3

2

+0.5×4

2

=

17