The switch in the circuit shown below is a two-way switch; to prevent sparking,

Question

The switch in the circuit shown below is a two-way switch; to prevent sparking, the switch is also a "make-before-break" switch, meaning that, in moving from a to b, the switch makes contact at ban instant before losing contact at a.   When the switch is in position a, the inductor L is in series with the battery and resistor Ra.   When the switch is in position b, the inductor L is in series with resistor Rb.

Assume that Ra = 10.0 ?, L = 4.0 H,  Rb = 20.0 ?, and VB = 100 V, and also assume that the switch is first moved to position b. After a long time, the switch is then moved to position a. Immediately after moving the switch to position a, what will be the absolute value of the rate of change of current in resistor Ra?]

Explanation / Answer

Imax = VB/Ra = 100/10 = 10 A

i = Imax*(1-e^(-t/T))

di/dt = -Imax*e^(-t/T)*(-1/T)

at t = 0

di/dt = Imax/(L/R)

= Imax*R/L

= 10*10/4

= 25 A/s

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