Lr Circuit Differential Equation. The solution of the differential equation ri l di dt v is. The relation obtained is the differential equation of the lr circuit.
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Initially the switch is open and is open and there is no current in the circuit. The solution of this differential equation is given by shown at right where i max is ε r. Assuming you have a constant voltage v driving a series connection of a resistor r and inductor l the differential equation for i will be d i t d t r l i t v l.
Initially the switch is open and is open and there is no current in the circuit.
The time required for the current flowing in the lr series circuit to reach its maximum steady state value is equivalent to about 5 time constants or 5τ. We will integrate the equation by taking proper limits of time t and current i. Initially the switch is open and is open and there is no current in the circuit. General solution of differential equation for an inductor in lr circuit result figure shows an inductance l a resistance r and a source of emf ε connected in series through a switch s.
