2000010806

Let’s have a coil of \(0.06\,\mathrm{H}\) inductance. The current flowing through the coil is given by \[ i=0.2\sin(100\pi t),\] where time \(t\) is measured in seconds and current \(i\) is measured in amperes. Determine the voltage induced in the coil at time \(t=2\) seconds. (Hint: Instantaneous voltage can be expressed as the derivative of current function with respect to time: \(u(t)=-L\frac{\mathrm{d}i}{\mathrm{d}t}\). The negative sign indicates only that voltage induced opposes the change in current through the coil per unit time. It does not affect the magnitude of the voltage.)