A charge Q = 4sin2πt/6 + 6cosπt/4 passes through a conductor. Find v

1.	A charge Q = 4sin2πt/6 + 6cosπt/4 passes through a conductor. Find value of current at time 4 second.
Answer» \(Q = 4 sin^2\pi t/6 + 6 cos\,\pi t /4\) \(i = \frac{d\theta}{dt}\) \(i = \frac d{dt} (4 sin^2\pi t/6+ 6cos\,\pi t/4)\) \(i = 4 \times 2sin \frac{\pi t}6 \times cos \frac{\pi t}6 \times \frac \pi 6 + 6x - sin \frac{\pi t }4 \times \frac \pi 4\) \(i = \frac{8\pi}6 sin \frac{\pi t}6 cos \frac{\pi t}6 - \frac{6\pi}4sin \frac{\pi t}4\) \(i = \frac {8\pi}6 \times sin(\frac{\pi \times 4}6) cos (\frac {\pi\times 4} 6) - \frac {6\pi }4\times 0\) \(i = \frac{8\pi}6 \times \frac {\sqrt3}2 \times \frac{-1}2\) \(= + \frac{\pi\sqrt 3}3\) \(i = + \frac\pi{\sqrt 3}\) ampere

A charge Q = 4sin2πt/6 + 6cosπt/4 passes through a conductor. Find value of current at time 4 second.

Answer»

\(Q = 4 sin^2\pi t/6 + 6 cos\,\pi t /4\)

\(i = \frac{d\theta}{dt}\)

\(i = \frac d{dt} (4 sin^2\pi t/6+ 6cos\,\pi t/4)\)

\(i = 4 \times 2sin \frac{\pi t}6 \times cos \frac{\pi t}6 \times \frac \pi 6 + 6x - sin \frac{\pi t }4 \times \frac \pi 4\)

\(i = \frac{8\pi}6 sin \frac{\pi t}6 cos \frac{\pi t}6 - \frac{6\pi}4sin \frac{\pi t}4\)

\(i = \frac {8\pi}6 \times sin(\frac{\pi \times 4}6) cos (\frac {\pi\times 4} 6) - \frac {6\pi }4\times 0\)

\(i = \frac{8\pi}6 \times \frac {\sqrt3}2 \times \frac{-1}2\)

\(= + \frac{\pi\sqrt 3}3\)

\(i = + \frac\pi{\sqrt 3}\) ampere