Question

Suppose that you have a circuit that has a resistance of 8 , an inductance of

4 and an EMT of 6e⁻²t cost. The initial current on the circuit was 18.
The initial charge on the circuit was 22. The following differential equation can
be used for your work

i(t)= dq/dt
L di/dt+Ri+q/C=E(t)
4. Or
5. q′′+R/L q′+1/ LC q=1/L1E(t)

Find the function that models the charge on the circuit.

Answer 1

The function that models the charge on the circuit can be found by integrating the given differential equation. The solution to the differential equation is q(t) = Qe^(-t/τ), where Q is the initial charge on the circuit and τ is the time constant of the circuit.

Step-by-step explanation:

The function that models the charge on the circuit can be found by integrating the given differential equation. The differential equation is:

q′′ + R/L q′ + 1/(LC) q = 1/(L1)E(t)

Integrating this equation will give you an equation for the charge on the circuit as a function of time.

The solution to the differential equation is:

q(t) = Qe^(-t/τ)

Where Q is the initial charge on the circuit, τ is the time constant of the circuit, and t is time.