DIFFERENTIATION2

DIFFERENTIATION2

1. The total charge entering a terminal is given by Q= 5t sin 4πt mC. Calculate the current at t=0.5s

2. i= dQ/dt

   • by applying PRODUCT RULE;
     • d/dt (5t sin 4πt) mC
       • u= 5t
         • du/dt= 5
           • i= u'v + v'u
             • i= (5) (sin 4πt) + (5t) (4π cos 4πt)
               • EXPAND!
                 • i= 5 sin 4πt + 20πt cos 4πt mA/s
                   • if t= 0.5s
                     • substitute (t= 0.5) in the equation;
                       • i= 5 sin 4π (0.5) + 20 (0.5)π cos4π (0.5) mA
                         • i= 5 (sin 2π) + 10π (cos 2π) mA
                           • i= 10π mA/s
       • v= sin 4πt
         • dv/dt= 4π cos 4πt