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LRC Circuit Problems

(See bottom of page for answers.)

1. Two capacitors and a coil connected in parallel are used to tune in frequencies from 500 to 1600 kHz.. If the inductance of the coil is 100 uH and the fixed capacitor is 80 pF, what is the range of the variable capacitor?

2. Why might wearing a bracelet in a region of strong magnetic field be hazardous?

3. A capacitor carries opposite 5.2 x10-6 C charges on its plates, and an electric field of 2x103 V/m between its plates. What is the area of each plate?

4. Two parallel aluminum-foil sheets, each 4.0 cm wide and 5.00 m long are separated by a Teflon strip 0.028 mm thick. Teflon’s dielectric constant is 2.1. What is this capacitor’s capacitance?

5. What capacitance is needed to store 25 µC in a capacitor with a 2.4 V potential difference between its plates?

6. A particular capacitor with a mica (k=5.4) dielectric stores 9.00mJ of energy when connected to a 3.00V source. What potential difference would be needed to store the same energy if this capacitor had an air dielectric?

7. A 3.40F capacitor carrying 5.50C and a 1.6F capacitor carrying 4.3C are connected in parallel with unlike charges together. Determine the final charge on the 3.4F capacitor.

8. What resistance is needed in series with a 10-uF capacitor at 1.0 kHz for a total impedance of 45 ohms?

9. Over a period of 1.5 sec a capacitor is charged to 63% of its maximum voltage in a single-loop RC circuit. Find the time constant for the circuit and the percentage of the circuit's maximum voltage after 15 sec.

10. What is the voltage across a 1.0 μF capacitor that is connected in series with a 2.0 μF capacitor and a 3.0 V battery?

11. What is the potential difference across a 120 μF capacitor that is storing 73 J of electric potential energy?

12. Capacitor plates separated by 0.38mm of air have a potential difference of 26 volts. If  each plate is 100 cm2, what are: (a) the capacitance, (b) the electric field strength between the plates, (c) the amount of charge stored on each plate?

13. Parallel 2.00-cm2 plates separated by 5.00 mm of air are connected across a 12.0 V battery.  How much energy do they store?

14. The current in an RL circuit reaches 95% max in 3.00 seconds.  If the inductance is .310 mH, what are the inductive time constant and resistance in the circuit?

15. A circuit with a 34.8 μF capacitor and an uncalibrated capacitor has a capacitance of 32.0 μF. What is the capacitance of the mystery capacitor? Is it in series or parallel with the first capacitor?

16. The potential difference across an isolated air-filled capacitor is 100 V.  When powder is placed between the capacitor’s plates, the potential difference across the capacitor is 20 V.  What is the dielectric constant of the powder?

17. A 5.00 microfarad capacitor initially charged to 24.0 V is connected positive-to-positive and negative-to-negative to a 6.0 microfarad capacitor initially charged to 12.0 V.  Find the final charges on the capacitors.

Selected solutions are printed below.

1.

C1 (fixed) and C2 (variable) are in parallel, so their combined capacitance is C1 + C2.

A resonant circuit has maximum current when 2πfL = 1/(2πfC), or

C = 1/(4π2f2L)

Since C = C1 + C2

C2 = 1/(4π2f2L) - C1

This will have to be solved twice: once for each frequency extreme.