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Consider a linear circuit having input voltage Vin (t) and a corresponding output voltage Vout (t). Which of the following statements concerning time varying input and output is certainly true: a) When the input is exponential Vin(t) = es₁t with some value $₁, the output must also be exponential Vout (t) = Aes2t with s2 and s₁ being different in general. b) When the input is exponential Vin(t) = esit with exponential constant S₁, the output must also be exponential

Consider a linear circuit having input voltage Vin (t) and a corresponding output voltage Vout (t). Which of the following statements concerning time varying input and output is certainly true: a) When the input is exponential Vin(t) = es₁t with some value $₁, the output must also be exponential Vout (t) = Aes2t with s2 and s₁ being different in general. b) When the input is exponential Vin(t) = esit with exponential constant S₁, the output must also be exponential

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**QUESTION 4** Consider a linear circuit having input voltage \( V_{\text{in}}(t) \) and a corresponding output voltage \( V_{\text{out}}(t) \). Which of the following statements concerning time varying input and output is certainly true: a) When the input is exponential \( V_{\text{in}}(t) = e^{s_1 t} \) with some value \( s_1 \), the output must also be exponential \( V_{\text{out}}(t) = Ae^{s_2 t} \) with \( s_2 \) and \( s_1 \) being different in general. b) When the input is exponential \( V_{\text{in}}(t) = e^{s_1 t} \) with exponential constant \( s_1 \), the output must also be exponential \( V_{\text{out}}(t) = Ae^{s_1 t} \) only if \( s_1 \) is a real number, while \( A \) could be either real or complex number. c) When the input is exponential \( V_{\text{in}}(t) = e^{s_1 t} \) with some exponential constant \( s_1 \), the output must also be exponential \( V_{\text{out}}(t) = Ae^{s_1 t} \), where both \( s_1 \) and \( A \) can be real or complex numbers. d) None of the above - ○ a) - ○ b) - ○ c) - ○ d)
Transcribed Image Text:**QUESTION 4** Consider a linear circuit having input voltage \( V_{\text{in}}(t) \) and a corresponding output voltage \( V_{\text{out}}(t) \). Which of the following statements concerning time varying input and output is certainly true: a) When the input is exponential \( V_{\text{in}}(t) = e^{s_1 t} \) with some value \( s_1 \), the output must also be exponential \( V_{\text{out}}(t) = Ae^{s_2 t} \) with \( s_2 \) and \( s_1 \) being different in general. b) When the input is exponential \( V_{\text{in}}(t) = e^{s_1 t} \) with exponential constant \( s_1 \), the output must also be exponential \( V_{\text{out}}(t) = Ae^{s_1 t} \) only if \( s_1 \) is a real number, while \( A \) could be either real or complex number. c) When the input is exponential \( V_{\text{in}}(t) = e^{s_1 t} \) with some exponential constant \( s_1 \), the output must also be exponential \( V_{\text{out}}(t) = Ae^{s_1 t} \), where both \( s_1 \) and \( A \) can be real or complex numbers. d) None of the above - ○ a) - ○ b) - ○ c) - ○ d)
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