There is no energy stored in the circuit in Figure at the time the switch is opened. a) Derive the differential equation that governs the behavior of i2 if L1 = 4 H, L2 = 16 H, M = 2 H, and R0 = 32 Ω. b) Show that when ig = 8 - 8e-t A, t ≥ 0, the differential equation derived in (a) is satisfied when i2 = e-t – e -2t A, t ≥ 0. c) Find the expression for the voltage v1 across the current source.
Sinusoids And Phasors
Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.
Circuit Theory
Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
There is no energy stored in the circuit in Figure at the time the switch is
opened.
a) Derive the differential equation that governs the behavior of i2 if L1 = 4 H, L2 =
16 H, M = 2 H, and R0 = 32 Ω.
b) Show that when ig = 8 - 8e-t A, t ≥ 0, the differential equation derived in (a) is
satisfied when i2 = e-t – e
-2t A, t ≥ 0.
c) Find the expression for the voltage v1 across the current source.
d) What is the initial value of v1 .Does this make sense in terms of known circuit
behavior?
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