Chapter 3, Problem 9PP

(Electrical eng.) a. Write, compile, and run a C++ program that calculates and displays the value of the current flowing through an RC circuit (see Figure 3.19). The circuit consists of a battery connected in a series to a switch, a resistor, and a capacitor. When the switch is closed, the current, i, flowing through the circuit is given by this formula:

$i=(EIR)e^{-t/RC}$

$\begin{array}{l}Eisthevoltageofthebatteryinvolts.\hfill \\ Risthevalueoftheresistorinohms.\hfill \\ Cisthevalueofthecapacitorinfarads.\hfill \\ tisthetimeinsecondsaftertheswitchisclosed.\hfill \\ eisEuler’snumber,whichis2.71828\left(roundedtofivedecimalplaces\right).\hfill \end{array}$

Using this formula, write, compile, and run a C++ program to determine the voltage across the capacitor shown in Figure 3.19 when t is 0.31 seconds. (Note: The value of RC is referred to as the system’s time constant.)

The program should prompt the user to enter appropriate values and use input statements to accept the data. In constructing the prompts, use statements such as “Enter the voltage of the battery.” Verify your program’s operation by calculating by hand the current for the following test data:

$\begin{array}{l}Testdataset1:Voltage=20volts,R=10ohms,RC=0.044,t=0.023seconds\hfill \\ Testdataset2:Voltage=35volts,R=10ohms,RC=0.16,t=0.067seconds\hfill \end{array}$

b. Check the value computed by your program by hand. After verifying that your program is working correctly, use it to complete the following chart: