# Derivatives and Integrals

1.) The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).

2.) Find the volume of the solid of revolution obtained by rotating the region bounded by y = cos x to the power 2, x=0, x = square root of (pi/2) and y = 0 about the y - axis.

3.) The voltage in a certain circuit is given by e(t) = E sin wt . Find the mean voltage over half a period.

Â© BrainMass Inc. brainmass.com December 24, 2021, 6:30 pm ad1c9bdddfhttps://brainmass.com/math/derivatives/derivatives-integrals-initial-voltages-118936

#### Solution Preview

Questions (Chapter 7 Integration Techniques).

1.) The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if

the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).

i = C dv/dt

2 Cos (100t) = 10^(-4) * dv/dt

dv = 20000 Cos (100t) dt

Integrate both sides,

v = (20000/100) Sin (100t) + K

at t=0, V = 0 ==> K = 0

Hence, v(t) = 200 Sin (100t)

at t=0.2 sec, v = 200 Sin(20 Radians) = ...

#### Solution Summary

Derivatives and integrals are found. The voltage of a certain circuit is determined.