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Question:

Published on: 21 November, 2024

At t=0, the instantaneous value of a 50 Hz, sinusoidal current is 5 Amp and increases in magnitude further. Its R.M.S value is 10 Amp.

Write the expression for its instantaneous value
Find the current at t=0.01 and t=0.015 sec.
Sketch the waveform indicating this value.

Answer:

The R.M.S value of sinusoidal current is I_R.M.S=10 Amp, thus the peak value of current

I_max=√2 ×I_R.M.S=10√2 Amp.

At t=0, the instantaneous value of current is i(t=0)=5 Amp.

Therefore the instantaneous value of current can be expressed as

i(t)=i(t=0)+I_max sin⁡ωt

i(t)=5+10√2 sin⁡ωt

i(t)=5+10√2 sin⁡2πft

i(t)=5+10√2 sin⁡2×50πt

i(t)=5+10√2 sin⁡100πt

The current at t=0.01 sec is

i(t=0.01)=5+10√2 sin⁡314×0.01

i(t=0.01)=5+10√2 sin⁡3.14 Amp

i(t=0.01)=5.775 Amp.

The current at t=0.015 sec is

i(t=0.01)=5+10√2 sin⁡314×0.015

i(t=0.01)=5+10√2 sin⁡4.71 Amp

i(t=0.01)=6.16 Amp.

The current waveform of the problem is given below

Fig. 4 waveform of sinusoidal wave with mentioned parametric values.

Subjects

Basic Electrical Engineering Radio Frequency and Microwave Engineering Power Electronics Electrical Engineering Management Analog Communication

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