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A conducting single-turn circular loop with a total resistance of 4.50 Ω is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by ΦB = a + bt2 − ct3, where a = 7.00 Wb, b = 12.5 Wb/s−2, and c = 5.50 Wb/s−3. ΦB is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 1.70 s?

Respuesta :

Answer:

Explanation:

Given

Resistance [tex]R=4.5\Omega [/tex]

Flux [tex]\phi =a+bt^2-ct^3[/tex]

[tex]\phi =7+12.5t^2-5.50t^3[/tex]

emf induced [tex]e=-\frac{d\phi }{dt}[/tex]

[tex]e=-\frac{d(7+12.5t^2-5.50t^3)}{dt}=25t-16.5t^2[/tex]

[tex]i=\frac{e}{R}=-\frac{1}{R}\times \frac{d\phi }{dt}[/tex]

[tex]i=\frac{1}{4.5}\times (25t-16.5t^2)[/tex]

Maximum value of will be at [tex]\frac{di}{dt}=0[/tex]

therefore

[tex]\frac{di}{dt}=0[/tex]

[tex]25-33t=0[/tex]

[tex]t=0.757 s[/tex]

i at [tex]t=0.757 s[/tex]

[tex]i=\frac{1}{4.5}\times (25\times 0.757-16.5(0.757)^2)[/tex]

[tex]i=2.104 A[/tex]

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