Transient Currents Suppose the circuit described by Eq. (9) is driven by a sinusoidal

Chapter 9, Problem 45

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Transient Currents Suppose the circuit described by Eq. (9) is driven by a sinusoidal voltage source V (t) = V sin t (where V and are constant). (a) Show that I (t) = V R2 + L22 (R sin t L cos t) + Ce(R/L) t (b) Let Z = R2 + L22. Choose so that Z cos = R and Z sin = L. Use the addition formula for the sine function to show that I (t) = V Z sin(t ) + Ce(R/L) t This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially

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