Question

The current through a wire depends on time as i = i0 + a sin pi t where i0 = 10 A, a = pi/2 find charge crossed through a section of wire in 3 seconds

Answer 1

Answer ⇒  The Current flows in three seconds is 33.14 C.

Explanation ⇒

i = i₀ + aSinπ/2

Now,

$q = \int\limits^3_0 {i_0} \, dt + \int\limits^3_0 {aSin\pi t} \, dt$

thus, $q = i_0\int\limits^3_0 {t^0} \, dt + a\int\limits^3_0 {Sin\pi t} \, dt$

Therefore,

$q = i_0[t]_0^3 + a[-Cos\pi t]^3_0$

$q = i_0[t]_0^3 - a[Cos\pi t]^3_0$

q = 10 × [3 - 0] - π/2 × [Cos3π - Cos0]

q = 30 - π/2[-1 -1]

q = 30 + π

q = 33.14 C

Hope it helps.

Answer 2

Answer:

Explanation

[tex][/tex]