Acting On Impulse
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Consider the circuit below:
This circuit is driven by a short pulse of voltage that closely approximates an impulse, v(t) \approx \lambda_0\delta(t), where \lambda_0 = 10^{-4} Volt-seconds.
Under these conditions, the resistor voltage v_{\rm R}(t) is measured and is approximated as v_{\rm R}(t) \approx e^{-10000t}u(t) Volts, where t is measured in seconds.
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Find an analytical expression for the current response i_{\rm L}(t) to the impulse input in terms of any subset of \lambda_0, R, and L.
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Using this, find the values of L and R in the circuit, including units.
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If the short voltage pulse driving the system were a rectangular pulse 1\mu{\rm s} long, what would its amplitude (in Volts) need to be in order to approximate an impulse? Is this pulse duration short enough to make the measured response be well-represented as an impulse response? Why or why not?
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