Basic Engineering Mathematics, Fifth Edition

324 Basic Engineering Mathematics

Now try the following Practice Exercise

PracticeExercise 138 Ratesof change

(answers on page 355)

1. An alternating current,iamperes, is given by
   i=10sin2πft,wherefis the frequency in
   hertz andtis the time in seconds. Determine
   the rate of change of current whent=12ms,
   given thatf=50Hz.


2. The luminous intensity,Icandelas, of a lamp
   is given byI= 8 × 10 −^4 V^2 ,whereVis the
   voltage. Find
   (a) the rate of change of luminous intensity
   with voltage whenV=100 volts.

(b) the voltage at which the light is increas-

ing at a rate of 0.5 candelas per volt.

3. The voltage across the plates of a capacitor at
   any timetseconds is given byv=Ve−t/CR,
   where V,C and R are constants. Given
   V=200V,C= 0. 10 μFandR=2M,find
   (a) the initial rate of change of voltage.
   (b) the rate of change of voltage after 0.2s


4. The pressurepof the atmosphere at heighth
   above ground level is given byp=p 0 e−h/c,
   wherep 0 is the pressure at ground level andc
   is a constant. Determine the rate of change of
   pressure with height whenp 0 = 1. 013 × 105
   pascals andc= 6. 05 × 104 at 1450 metres.