Question

Formulate the differential equation representing the relationship of current (i), voltage (v), inductance(L) and time t.

Answer 1

Solution:

The (variable) voltage across the resistor is given by:

$V_{R}=i R$

The (variable) voltage across the inductor is given by:

$V_{L}=L \frac{d i}{d t}$

Kirchhoff's voltage law says that the directed sum of the voltages around a circuit must be zero. This results in the following differential equation:

$R i+L \frac{d i}{d t}=V$

where current (i), voltage (v), inductance(L) and time t.

This is the required D.E.