Question

The charge moving along a wire is governed by the charge equation q = 3t sin (30πt) C, determine the current at t = 300 μs

Answer 1

$q=3tsin(30\pi t)\\i=\frac{dq}{dt}$

$i=\frac{d}{dt}(3tsin(30\pi t))$

$$i=3sin(30\pi t)+90\pi t cos(30\pi t)$$

Put t value

$$i=3sin(30\pi \times300\times 10^{-6})+90\pi \times300\times 10^{-6}cos(30\pi\times300\times10^{-6} )$$

$$i=0.08481+0.08474=0.1695Amp$$