Using Kirchhoff's Current Law (KCL), determine the voltage developed across the coil in the figure shown.

Given i2 = 5e−2t; i4 = 3 sin t; and v3 = 4e−2t

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MPPKVVCL Indore JE Electrical 21 August 2018 Official Paper
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  1. 3 cos t − 22e−2t
  2. 12 cos t − 88e−2t
  3. 3 cos t + 22e−2t
  4. 12 cos t + 88e−2t

Answer (Detailed Solution Below)

Option 2 : 12 cos t − 88e−2t
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Detailed Solution

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Concept

The voltage across the inductor coil is given by:

where, L = Inductor

 Rate of change of current across the inductor

The current across the capacitor is given by:

where, C = Capacitor

 Rate of change of voltage across the capacitor

Calculation

Given i2 = 5e−2t; i4 = 3 sin t; and v3 = 4e−2t

KCL states that “The algebraic sum of all incoming current is equal to the algebraic sum of all outgoing current at a node.” 

Applying KCL at node A, we get:

Sum of incoming current = Sum of outgoing current

The voltage across the inductor coil is given by:

V12 cos t − 88e−2t

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