VR (V) 25.0 20.0 15.0 10.0 5.0 0.0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 (ms)
You are studying a solenoid of unknown resistance and inductance. You connect it in series with a 50.0 Ω resistor, a 25.0 V battery that has negligible internal resistance, and a switch. Using an ideal voltmeter, you measure and digitally record the voltage vR across the resistor as a function of the time t that has elapsed after the switch is closed. Your measured values are shown in Fig. P30.68, where vR is plotted versus t. In addition, you measure that vR = 0 just after the switch is closed and vR = 25.0 V a long time after it is closed. (a) What is the resistance RL of the solenoid? (b) Apply the loop rule to the circuit and obtain an equation for vR as a function of t. (c) According to the equation that you derived in part (b), what is vR when t = t, one time constant? Use FIG to estimate the value of t = t. What is the inductance of the solenoid? (d) How much energy is stored in the inductor a long time after the switch is closed?
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