The maximum values of the alternating voltage and current are 400 V and 20 A, respectively, in a circuit. The frequency of the alternating quantities is 50 Hz, and these quantities are sinusoidal. The phase angle of the current with respect to voltage is θ. Choose the correct expression for the voltage and current with respect to time t

Question

Question

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SSC JE EE Previous Paper 12 (Held on: 24 March 2021 Evening)

v(t) = 400sin(100πt) V, i(t) = 20 sin(100πt) A
v(t) = 400sin(100πt) V, i(t) = 20 sin(100πt + θ) A
\(v(t) = \frac{400}{\sqrt{2}} sin(100πt) V, i(t) = \frac{20}{\sqrt{2}} sin((100 + θπ )t) A\)
\(v(t) = \frac{400}{\sqrt{2}} sin(100πt) V, i(t) = \frac{20}{\sqrt{2}} sin(100πt) A\)

Answer 1

Concept:

General representation of AC voltage and current is given by

V = V_m sinωt

I = I_m sin(ωt + θ)

where

V_m = Maximum value of voltage

I_m = Maximum value of current

θ = phase angle of current with respect to voltage

F1 Harish Battula 21-5-2021 Swati D14

Calculation:

Given:

V_m = 400 V , I_m = 20 A , f = 50 HZ

ω = 2πf = 2π × 50 = 100π

By substituting the values in general representation

V = 400 sin 100πt

I = 20 sin (100πt + θ )