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Signal Energy and RC Circuits

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The signal x(t) = e^(-|t|) is defined for all values of t.

(a) Plot the signal x(t) and determine if this signal is finite energy.

(b) If you determine that x(t) is absolutely integrable, could you say that x(t) has finite energy? Explain why or why not.
Hint: Plot |x(t)| and |x(t)|^2 as functions of time.

(d) To discharge a capacitor of 1 mF charged with a voltage of 1 volt we connect it, at time t=0, with a resistor of R Ohm. When we measure the voltage in the resistor we find it to be V_R(t) = e^-t u(t). Determine the resistance R. If the capacitor has a capacitance of 1 uF, what would be R? In general, how are R and C related?

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