# Practice Problems with resonant circuits.

1. A series RL circuit containing a 0.17-H inductor has a time constant of 0.13 s. What is the resistance in the circuit?

2. A 1000-ohm's resistor is joined in series with a 400-mH inductance and a 12-V battery. (a) What is the time constant of the circuit? (b) How long will it take after the circuit is completed for voltage across the resistor to reach 3.0 V?

3. A 250-microF capacitor is discharged through a 4.7-Mohm's resistance. What is the time constant?

4. A 5000-ohm's resistor is joined in series with a 100-microF capacitor. (a) What is the capacitive time constant of this combination? (b) If a 9.0-V battery is suddenly connected across the RC combination, how long will it take for the capacitor voltage to reach 8.0 V?

5. A radio circuit carries a sinusoidal current with a peak of 15.1 mA. What is the effective value of the current?

6. What is reactance of a 1.0-microF capacitor at a frequency of (a) 60 Hz, (b) 500 Hz, (c) 1000 Hz, and (d) 10 kHz?

7. An inductor has an inductance of 25mH. What is the reactance of this inductor at frequencies of 60, 1000, and 10,000 Hz?

8. A series circuit has R = 33 O, L = 0.15 H, and C = 110 microF across a 60-Hz sinusoidal voltage source with a peak value of 18-V. (a) What is the peak voltage across each of these elements? (b) What is the peak voltage across the combination of these elements? (c) What is the current in the circuit? (d) What is the phase angle between voltage and current?

#### Solution Preview

1. The time constant t = L/R seconds ==> R = L/t = 0.17/0.13 = 1.31 Ohms

2. t = 0.4/1000 = 4*10^-4 sec

When it reaches 3V across the resistor, the circuit current will be,

3/1000 = 3mA

We have I = (V/R) * [1 - Exp(-R/L)t]

Or, 3/1000 = (12/1000)*[1 - Exp(-1000/0.4)t]

1 = 4 [1 - Exp(-1000/0.4)t]

= 4 * [1 - Exp(-2500)t]

[1 - Exp(-2500)t] = 0.25 ====> Exp(-2500)t = 0.75

Taking log on both sides.. ==>-2500t = -0.1249

==> t = 0.00004996 Second = 49.96 micro seconds

3. The product R C is called the "time ...

#### Solution Summary

A good and well explained set of practice problems involving resistors, capacitors and inductors.