Question

What is the differential equation governing the growth of current in the circuit as a function of time after t=0? express the right-hand side of the differential equation for di(t)dt in terms of i(t), vb, r, and l?

Answer 1

Answer:

$v_{b}=ir+L\frac{di}{dt}$

Explanation:

A differential equation that contain a term with di(t)/dt is in a RL circuit. Here we have

$v_{b}=v_{r}+v_{i}$

where vr is the voltage in the resistance, vi is the voltage in the inductance and vb is the source voltage. But also we have that

$v_{r}=ir\\v_{i}=L\frac{di}{dt}$

where L is the inductance of the circuit, r is the resistance an i is the current. By replacing we have the differential equation

$v_{b}=ir+L\frac{di}{dt}$

I hope this is useful for you

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