Question

A series circuit contains a resistor and an inductor as shown in the figure. Determine a differential equation for the current i(t) if the resistance is R, the inductance is L, and the impressed voltage is E(t). (Use i for i(t) and E for E(t)).

Answer 1

From the information given, the differential equation will be di/dt = (E - Ri) / L.

How to calculate the differential equation

From the information given, we can set up the differential equation as:

-E(t) = Ldi(t)/Dr + Ti(t) = 0.

Here, i(t) = I

E(t) = E

Therefore, this will be:

= -E + Ldi/dt + Ri = 0

We'll now solve for di/dt

Ldi/dt = E - Ri

di/dt = (E - Ri) / L

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