DC Source

Let us assume that the source voltage is dc and is given by ν_s = V_dc . Then the line current is given by the differential equation

(6.1)

The solution of the above equation is written in the form

(6.2)

Since the initial current i (0) = 0 and since ν_s ( τ ) = V_dc for 0 £ t < ¥ , we can rewrite the above equation as

(6.3)

where T = L / R is the time constant of the circuit.

Let us assume R = 1Ω , L = 10 mH and V_dc= 100 V. Then the time response of the current is as shown in Fig. 6.2. It can be seen that the current reaches at steady state value of 100 A. The time constant of the circuit is 0.01 s. This is defined by the time in which the current i ( t ) reaches 63.2% of its final value and is obtained by substituting t = T. Note that the slope of the curve is given by

(6.4)

Fig 6.2 Current in the R-L circuit when the source is dc