An alternating current of frequency 60Hz has maximum value of 120A. (1) write down the equation for…

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An alternating current of frequency 60Hz has maximum value of 120A. (1) write down the equation for instateneous value. (2) recording the time from instant the current is zero and becoming positive find the instateneous time after 1/360 second

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Haya Jozee, hebu tutatue hili. a) Andika mlinganyo wa thamani ya papo hapo. Step 1: Tambua vigezo vilivyotolewa. Tunapewa: Thamani ya juu zaidi ya mkondo (maximum current), I₀ = 120 A; Marudio (frequency), f = 60 Hz Mkondo unaanzia sifuri na kuwa chanya, hivyo tunatumia kazi ya sine. Step 2: Andika mlinganyo wa jumla wa mkondo wa papo hapo. Mlinganyo wa mkondo wa papo hapo (instantaneous current) ni: I = I₀ sin(2π ft) Step 3: Badilisha thamani za I₀ na f kwenye mlinganyo. I = 120 sin(2π × 60t); I = 120 sin(120π t); Mlinganyo wa thamani ya papo hapo ni I = 120 sin(120π t). b) Tafuta mkondo wa papo hapo baada ya sekunde 1/360. Step 1: Tumia mlinganyo kutoka sehemu (a). I = 120 sin(120π t); Step 2: Badilisha thamani ya muda t = 1/360 s kwenye mlinganyo. I = 120 sin(120π × 1/360) Step 3: Rahisisha na kokotoa thamani ya I. I = 120 sin((120π)/(360)); I = 120 sin((π)/(3)); Tunajua kuwa sin((π)/(3)) = sin(60°) = (√(3))/(2). I = 120 × (√(3))/(2); I = 60√(3) A Thamani ya mkondo wa papo hapo ni 60√(3) A.

An alternating current of frequency 60Hz has maximum value of 120A. (1) write down the equation for instateneous value. (2) recording the time from instant the current is zero and becoming positive find the instateneous time after 1/360 second

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Step-by-step solution

Part a· 3 steps

Tambua vigezo vilivyotolewa.

Andika mlinganyo wa jumla wa mkondo wa papo hapo.

Badilisha thamani za $I_0$ na $f$ kwenye mlinganyo.

Part b· 3 steps
$60\sqrt{3} \text{ A}$

Tumia mlinganyo kutoka sehemu (a).

Badilisha thamani ya muda $t = \frac{1}{360} \text{ s}$ kwenye mlinganyo.

Rahisisha na kokotoa thamani ya $I$ .

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An alternating current of frequency 60Hz has maximum value of 120A. (1) write down the equation for instateneous value. (2) recording the time from instant the current is zero and becoming positive find the instateneous time after 1/360 second

Answers

Step-by-step solution

Part a· 3 steps

Tambua vigezo vilivyotolewa.

Andika mlinganyo wa jumla wa mkondo wa papo hapo.

Badilisha thamani za I0I_0I0​ na fff kwenye mlinganyo.

Part b· 3 steps603 A60\sqrt{3} \text{ A}603​ A

Tumia mlinganyo kutoka sehemu (a).

Badilisha thamani ya muda t=1360 st = \frac{1}{360} \text{ s}t=3601​ s kwenye mlinganyo.

Rahisisha na kokotoa thamani ya III.

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Badilisha thamani za $I_0$ na $f$ kwenye mlinganyo.

Part b· 3 steps
$60\sqrt{3} \text{ A}$

Badilisha thamani ya muda $t = \frac{1}{360} \text{ s}$ kwenye mlinganyo.

Rahisisha na kokotoa thamani ya $I$ .