Problems

1. An air-core coil has a self-inductance of 0.056 henry, and a resistance of 9.2 ohms. Calculate the Q at 100, 1000, 10,000, 1,000,000, and 10,000,000 cycles. Plot as a curve. Would measured values agree with calculated values? Why?

2. If the coil just considered is connected in series with a 0.5-microfarad capacitor, what will be the resonant frequency? What will be the impedance at resonance, and at 10 per cent above and below resonance?

3. Repeat Problem 2 for the inductor and capacitor in parallel. Use both equations 15 and 16, and compare.

4. An oscillator has an open-circuit voltage of 39 volts at 1000 cycles and an internal impedance of 0.003 henry inductance and 447 ohms resistance. It is connected to the primary of a coil having an inductance of 0.052 henry and a resistance of 56 ohms. The mutual inductance between the primary and the secondary is 0.0536 henry. The secondary has an inductance of 0.061 henry, a resistance of 61 ohms, and is connected to a 500-ohm load resistor. Calculate the current that will flow through this resistor.

5. If the combination of Problem 2 is connected across 50 volts at the resonant frequency, what will be the line current, and the voltage across the inductor and across the capacitor?

6. If the combination of Problem 3 is connected in parallel and across 50 volts at the resonant frequency, what will be the line current, and the current through the inductor and capacitor?

7. Prove mathematically that the statement in italics preceding equation 24 is correct.

8. Prove mathematically that the statement in italics following equation 29 is correct.

9. Repeat the problems starting on page 72 for increasing and decreasing impedances, but with frequencies of 2.0 megacycles instead of 5.0 megacycles, and at 7.5 instead of 10.0 megacycles.

10. The heater of a thermocouple has a constant resistance of 610 ohms. For a current of 0.002 ampere through the heater, the deflection of the associated microammeter is 10 microamperes. The thermocouple heater is placed in series with 9390 ohms, and placed across an unknown voltage. The microammeter reads 100 microamperes. What is the value of the unknown voltage in volts?