Consider the simple series RC circuit shown. The switch is closed at t= 0. a) Us
ID: 1436617 • Letter: C
Question
Consider the simple series RC circuit shown.
The switch is closed at t= 0.
a) Using the given numbers write down the equation for current as a function of time.
b) Write the power output of the battery as a function of time.
c) integrate the above equation from t=0 to infinity to find the total energy output of the battery while the capacitor is changing.
d) Calculate the energy stored on the capacitor once it is fully charged.
e) Write down the equation for the power dissipated by the resistor as a function of time.
f) Integrate this equation from t=0 to infinity to find the total energy dissapated by the resistor.
Explanation / Answer
Here,
a)
time constant , T = R *C
T = 200 * 30 * 10^-3
T = 6 s
maximum current , I = E/R = 50/200 A
I = 0.25 A
the current in the circuit is
I = 0.25 * e^(-t/6) A
b)
for the power output of battery
P = E * I
P = 50 * 0.25 * e^(-t/6) W
P = 12.5 * e^(-t/6) W
the power output is 12.5 * e^(-t/6) W
c)
for the total energy output
total energy output = integrate(12.5 * e^(-t/6) dt) from 0 to infinite
total energy output = -12.5 * 6 * (e^(-t/6)) from 0 to infinite
total energy output = 75 J
d)
energy stored in energy when it is fully charged = 0.5 * C * V^2
energy stored in energy when it is fully charged = 0.5 * 0.030 * 50^2
energy stored in energy when it is fully charged = 37.5 J
the energy stored in energy when it is fully charged is 37.5 J