Time Limit: 2 Seconds
Memory Limit: 65536 KB
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 ω t and v2 = VR
cos ( ω t + θ ) where VS is the voltage of the source, ω is the frequency (in
radians per second), and t is time. VR is the magnitude of the voltage drop
across the resistor, and θ is its phase.
You are to write a program to determine VR for different values
of ω. 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 – 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
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
Source: Greater New York 2001