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If V=100sin (100t)V and I =100sin (100t+...

If V=100sin (100t)V and I =100sin `(100t+(pi)/(3))` mA are the instantaneous values of voltage and current, then the rms values of voltage and current are respectively

A

`70.7 V, 70.7 mA`

B

`70.7 V, 70.7 A`

C

`141.4 V,141.4 mA`

D

`100 V,100 mA`

Text Solution

Verified by Experts

The correct Answer is:
A
The instantaneous value of voltage is
V = 100 sin (100t) V
Compare it with, `V=V_(0) sin(omega t)V`
we get, `V_(0)=100 V, omega = 100 "rad " s^(-1)`
The rms value of voltage is
`V_("rms")=(V_(0))/(sqrt(2))=(100)/(sqrt(2))V=70.7 V`
The instantaneous value of current is
`I = 100 sim (100 t +(pi)/(3))mA`
Compare it with, `I = I_(0)sin (omega t+phi)`
we get, `I_(0) = 100 mA, omega = 100 "rad " s^(-1)`
The rms value of current is
`I_("rms")=(I_(0))/(sqrt(2))=(100)/(sqrt(2))mA=70.7 mA`
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