Examples for AC circuits

Example #1

Problem:

Consider the LC circuit to the right. If one needs to tune this circuit to a frequency of 84 kHz, and the capacitor has a capacitance C = 3.0 mF, what inductance L is needed?

Solution:

Use the relation, . Solve for L.

L = 1.20E-6 H

Example #2

Problem:

a.) What is the impedance of the circuit to the right if: f = 60 Hz, L = 20 mH, R = 4.0 W?

Solution:

Z = 8.54 W

b.) If the r.m.s. voltage of the source is V_rms = 110 V, what is the r.m.s. current?

Solution: I_rms = V_rms/ Z

I_rms = 12.9 amps

c.) What is the peak current?

Solution: I_p = sqrt(2) ·I_rms

I_p = 18.2 amps

d.) What is the power dissipated in the resistor?

Solution: P = I²_rms·R

P = 1320 W

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