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Question

The switch was in position (1) for long time and was moved to position (2) at t=0 is
d2idt2 at t=0+


A
1000A/sec2
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B
1000A/sec2
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C
11500A/sec2
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D
11500A/sec2
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Solution

The correct option is C 11500A/sec2
Switch is in position (1) in steady state


I=5V2.5kΩ=2mA

Now switch is moved to position (2)


Applying KVL in the circuit, we get
iR+Ldidt+1Cidt=0
At, t=0+,i(0+)=I=2mA
1Cidt=0
IR+Ldidt=0____(i)
didt=IRL=2mA×2.5kΩ1H=5A/sec
Differentiating equation (i)
Rdidt+Ld2idt2+1Ci=0
At, t=0+
2.5×103×(5)+1×d2idt2+2×1032×106=0
12.5×103+d2idt2+1×103=0
d2idt2=11.5×103A/sec2
d2idt2 t=0+=11500A/sec2

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