Question

the magnetic flux through the coil is varying according to relation ∅=5t³+4t²+2t-5. calculate the induced current through the coil at t=2sec, if resistance of coil is 5 oh
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Answer 1

Answer:

Explanation:

here you go

Answer 2

Solution:-

Given

$\rm \phi = 5 {t}^{3} + 4 {t}^{2} + 2t - 5$

$\rm \: t \: = 2sec \:$

$\rm \: resistance = 5 \Omega$

Differentiate magnetic flux with respect to time

$\rm \: induced \: emf \: = \dfrac{d \phi}{dt}$

$\rm \: \dfrac{d \phi}{dt} = \dfrac{d(5 {t}^{3} + 4t {}^{2} + 2t - 5)}{dt}$

$\rm \: = {(15 {t}^{2} + 8t + 2) }{}$

When at t = 2 sec

we get

$\rm \: 15 \times (2) {}^{2} + 8 \times 2 + 2 = 78v$

Using formula

$\boxed{ \rm \:E = IR }$

$\rm \: E = 78v$

$\rm \: R = 5 \Omega$

Put the value

$\rm \: 78 = I \times 5$

$\rm \: I = \dfrac{78}{5} = 15.6A$

So induced current is 15 .6 A