Consider the AC circuit below. We will assume that the circuit is in steady-state. Thus, the voltage at nodes 1 and 2 are given by v1 = VS cos ¦Ø t and v2 = VR cos ( ¦Ø t + ¦È ) where VS is the voltage of the source, ¦Ø is the frequency (in radians per second), and t is time. VR is the magnitude of the voltage drop across the resistor, and ¦È is its phase.
You are to write a program to determine VR for different values
of ¦Ø. You will need two laws of electricity to solve this problem. The first
is Ohm's Law, which states v2 = i R where i is the current in the circuit, oriented
clockwise. The second is i = C d/dt (v1 ¨C v2) which relates the current to the
voltage on either side of the capacitor. "d/dt" indicates the derivative with
respect to t.
The input will consist of one or more lines. The first line contains three real numbers and a non-negative integer. The real numbers are VS, R, and C, in that order. The integer, n, is the number of test cases. The following n lines of the input will have one real number per line. Each of these numbers is the angular frequency, ¦Ø.
For each angular frequency in the input you are to output its corresponding VR on a single line. Each VR value output should be rounded to three digits after the decimal point.
1.0 1.0 1.0 9 0.01 0.031623 0.1 0.31623 1.0 3.1623 10.0 31.623 100.0
0.010 0.032 0.100 0.302 0.707 0.953 0.995 1.000 1.000