Give expressions for the sine-wave voltage signals...

Give expressions for the sine-wave voltage signals having: (a) $10-\mathrm{V}$ peak amplitude and $10-\mathrm{kHz}$ frequency (b) $120-\mathrm{V} \mathrm{rms}$ and $60-\mathrm{Hz}$ frequency (c) $0.2-\mathrm{V}$ peak-to-peak and 1000 -rad/s frequency (d) $100-\mathrm{mV}$ peak and $1-\mathrm{ms}$ period

Transcript

00:01 Here in the a part given the peak voltage is given that is vm or maximum voltage is equal to 10 volt the frequency is given 10 into 10 power 3 hertz we know that omega is equal to that angular velocity is equal to 2 pi into frequency this relation is to be known so here the expression for voltage at an instant time t is equal to maximum voltage into sine omega t what this is equal to maximum voltage is 10 volt into sine instead of omega you can write 2 pi into frequency frequency is 10 into 10 power 3 hertz into t or this is equal to 10 sine 2 pi into 10 power 4 t so this is the expression of voltage at time t.

01:07 Now we are moving on to the next part b part here given that the rms voltage is given vrms is equal to 120 voltage.

01:20 So from here we need to calculate the maximum voltage.

01:24 The relation between maximum voltage and rms voltage is given by vm is equal to root 2 times vrms.

01:32 This is equal to 1.

01:34 Root 2 into 120.

01:36 Upon multiplying we will get the value of peak voltage to be 169 .71 volt.

01:44 This is the peak voltage.

01:48 The frequency also given in the question which is 60 hertz.

01:52 Therefore the expression for v of t is equal to peak voltage into zine into omega t, where omega is equal to 2 pi into frequency or this becomes instead of vm we are writing 169 .71.

02:10 Sine into 2 .5 .5 .60 which is the frequency into t.

02:17 Upon solving we will get the expression for v of t is equal to 169 .71 into sine 120 pi t.

02:30 So this will be the expression for part b.

02:33 Now we are moving on to the next part, c part here given.

02:41 The peak to peak voltage is given, that is vpp is equal to 0 .2 volt...

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