Question

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?

Answer 1

Step-by-step explanation:

Given

Resistance
`R=4.5\Omega`

Flux
`\phi =a+bt^2-ct^3`

`\phi =7+12.5t^2-5.50t^3`

emf induced
`e=-(d\phi )/(dt)`

`e=-(d(7+12.5t^2-5.50t^3))/(dt)=25t-16.5t^2`

`i=(e)/(R)=-(1)/(R)* (d\phi )/(dt)`

`i=(1)/(4.5)* (25t-16.5t^2)`

Maximum value of will be at
`(di)/(dt)=0`

therefore

`(di)/(dt)=0`

`25-33t=0`

`t=0.757 s`

i at
`t=0.757 s`

`i=(1)/(4.5)* (25* 0.757-16.5(0.757)^2)`

`i=2.104 A`