Homework SourseIn the circuit shown below a battery supplies a constant vol
In the circuit shown below, a battery supplies a constant voltage of 40V.
Given the inductance L=2H and R=10?, obtain the following:
Part a) The differential equation that represents the RL circuit.
Part b) The general solution for the current that flows through the RL circuit.
Hint: Use your knowledge of circuit theory to obtain the differential equation. Remember that the voltage drop across the inductor is given LdI/dt.
Given the inductance L=2H and R=10?, obtain the following:
Part a) The differential equation that represents the RL circuit.
Part b) The general solution for the current that flows through the RL circuit.
Hint: Use your knowledge of circuit theory to obtain the differential equation. Remember that the voltage drop across the inductor is given LdI/dt.
Solution
(a) 2 (dI/dt) + 10I = 40
(dI/dt) + 5I = 20
(b) - In (4 - I) = 5t + c
I = 4 - k(e^-5t)
where k is a general constant.
