An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled by the differential equation R dq/dt +1/C q = E(t), where R and C are constants (resistance and capacitance) and q = q(t) is the amount of charge on the capacitor at time t. For simplicity in the following analysis, let R = C = 1, forming the differential equation dq/dt + q = E(t). In Exercises 17–20, an electromotive force is given in piecewise form, a favorite among engineers. Assume that the initial charge on the capacitor is zero [q(0) = 0]. (i) Use a numerical solver to draw a graph of the charge on the capacitor during the time interval [0, 4]. (ii) Find an explicit solution and use the formula to determine the charge on the capacitor at the end of the four-second time period. E(t)=5 if 0=2
Sinusoids And Phasors
Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.
Circuit Theory
Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
An electric circuit, consisting of a capacitor, resistor, and
an electromotive force can be modeled by the differential
equation
R dq/dt +1/C q = E(t),
where R and C are constants (resistance and capacitance) and
q = q(t) is the amount of charge on the capacitor at time
t. For simplicity in the following analysis, let R = C = 1,
forming the differential equation dq/dt + q = E(t). In Exercises 17–20, an electromotive force is given in piecewise form,
a favorite among engineers. Assume that the initial charge on
the capacitor is zero [q(0) = 0].
(i) Use a numerical solver to draw a graph of the charge on
the capacitor during the time interval [0, 4].
(ii) Find an explicit solution and use the formula to determine
the charge on the capacitor at the end of the four-second
time period.
E(t)=5 if 0<t<2
E(t)=0 if t>=2
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
