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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, 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 (100 t) 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)/(sqrt2) = (100)/(sqrt2) V = 70.7 V`
The instantaneous value of current is
`I = 100sin (100t + pi/3) mA`
Compare it with
`I = I_0 sin (omega t + phi)`
we get , `I_0 = 100mA , omega = 100 rad s^(-1)`
The rms value of current is
`I_(rms) = (I_0)/(sqrt2) = (100)/(sqrt2) mA = 70.7 mA`
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