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Circuit With Inductance and Resistance OnlyAuthor: E.E. Kimberly
In a circuit containing only R and L, as in Fig. 811 (a), let the circuit be closed at any time t, as in Fig. 811 (b), corresponding to the angle ϕ after the voltage v is zero and about to rise in a positive sense. The initial current will be zero, inasmuch as the circuit contains inductance which will prevent an instantaneous rise of current. The initial current may be thought of as being composed of a steadystate component iss and a transient component it which are equal and opposite immediately after the circuit is closed. Thus,
Therefore, and is negative at t=0. The angle ϕ is .The transient current it is of the same magnitude but is positive in sign when t = 0. The condition for dynamic stability is from which The total current is
When t = 0, i = 0 and the equation becomes and Therefore, (817)
Example 84.  A circuit having the constants R = 100 ohms and L = 0.5 henry is switched to a 60cycle supply of 220 volts at the instant when the voltage is zero
. What will be the magnitude of the current 0.00417 second after the circuit is closed? Solution.  In equation (817), Vm = 310, Z = 213.6, ω = 377, ϕ = 0, θ = 62°, and t=0.00417. Hence,


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