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B4. Referring to the R-L circuit in Fig. B4, an inductor, with internal resistance \( R 3=10 \Omega \), will be charged when the switch \( S W \) is closed at \( t=0 \) s. Fig. B4 Determine: (a) the time constant \( \tau \); (b) the equation for voltage \( v_{L} \) in terms of \( t \); (c) the time for \( v_{L} \) to reach its steady state; (d) the equation for current it in term of \( t \); and (e) the current \( i_{L} \) flowing through the inductor \( L \) at \( t=0, \tau, 2 \tau, 3 \tau, 4 \tau \) and \( 5 \tau \). (f) Plot the graph of current \( i_{L} \) against time \( t \) from \( t=0 \) to \( 5 \tau \). (g) Calculate the new value of \( \mathrm{L} \) if the time for the current is to reach its steady is shorten to \( 15 \mathrm{~ms} \).

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