Chapter 4: Q61P (page 1017)
During a summer internship as an electronics technician, you are asked to measure the self-inductance L of a solenoid. You connect the solenoid in series with a 10.0 Ω resistor, a battery that has negligible internal resistance, and a switch. Using an ideal voltmeter, you measure and digitally record the voltage vL across the solenoid as a function of the time t that has elapsed since the switch is closed. Your measured values are shown in Figure below, where vL is plotted versus t. In addition, you measure that vL = 50.0 V just after the switch is closed and vL = 20.0 V a long time after it is closed. (a) Apply the loop rule to the circuit and obtain an equation for vL as a function of t. (b) What is the emf E of the battery? (c) According to your measurements, what is the voltage amplitude across the 10.0 Ω resistor as t → ∞? Use this result to calculate the current in the circuit as t → ∞. (d) What is the resistance RL of the solenoid? (e) Use the theoretical equation from part (a), Fig below, and the values of E and RL from parts (b) and (d) to calculate L.
Short Answer
- the variation of voltage across solenoid is represented by equation:
b. the EMF of the battery is 50 volts.
c. the voltage drop across resistor is 30 volts and the current through resistor is 3 amperes.
d. the resistance of the solenoid is 6.7 ohms.
e. the self-inductance of the coil is 38.41 milli-henry.