1. [20%] The inductive time constant. In is given by: L IRL: E- ['11] Measurements are made using the circuit shown in Figure 1. By analyzing the rise time of the voltage across the resistor. limb the time constant rim is determined {in units of microseconds} for several different values of R [measured in Ohms]. Describe a plot that could be used to determine the value of the inductor L {in units of milihenrys]. Figurel 2. [20%] The components listed in Table 1 are at your disposal. A band-pass lter [as shown in Figure 2} is to be but. Identifyr which resistor should be used in the circuit to pass the narrowest possible band of frequencies drug. Justify your answer. Inductors (mi) Resistors (() Capacitors (uf) L = 100 R1 = 100 C1 = 0.02 R2 = 1,000 C2 = 0.1 R3 = 5, 100 C7 = 1 R4 = 10,000 C3 = 10 C4 = 100 C5 = 470 Table 1: Components that are available for building a band-pass filter. C L 6000 Vin N R. Vout Figure 2: A schematic of an LCR circuit that can be used as a "band-pass" filter. 3. [20%] Identify which capacitor should be used in the circuit to achieve the highest possible reso- nant frequency wo. Justify your answer. 4. [20%] Using the values for L, R, and C chosen in the previous two exercises, compute the theoreti- cal natural frequency wo of the circuit. 5. [20%] Convert the angular frequency wo (which has units of radians per second) above into an observable frequency fo with units of Hertz (or cycles per second)