Lecture 6 IV AC SERIESPARALLEL CIRCUITS VOLTAGECURRENT DIVIDER

Lecture 6 (IV): AC SERIES/PARALLEL CIRCUITS, VOLTAGE/CURRENT DIVIDER

OBJECTIVES 1. Compute the total circuit impedance for series RLC circuits. 2. Explain the effects of frequency changes on RLC circuit response. 3. Determine circuit voltages and currents in series RLC circuits. 4. Compute voltage drops across components in an RLC circuit using the voltage divider formula.

Ex: The source is a cosine function with ω=2000. Find Ix in time domain.

Answer

Ex: Find Z 1 and Z 2

Answer

Ex: Find i(t)

Different waveform of VS • VS 1 and VS 2 are different: • When analyzing ac circuit, it is expedient to express both signals as either Sine or Cosine.

Change the waveform of VS 1 • Using identity:

Changing Cos to Sine:

Redraw the circuit

Elements in Frequency domain • =4 rad/s Time domain Freq domain

Find The Current

Answer j 100

(b) Find the vc(t), v. L(t) • Use voltage divider

(c) Find the ic(t), i. L(t)

(d) Sketch the waveform for vc(t), v. L(t), ic(t), i. L(t)

Ex: Find ZT, IT, VC 2, P Z 2

Solution • Find the total impedance: • Then, the total current is:

Solution P = VI cos (q. T) = (10 V)(461 m. A) cos(-42. 4 o) = 3. 40 m. W

TOOLS • Note from the previous examples, all of our tools from DC work: – Ohm’s Law – Voltage Divider – Current Divider – Kirchoff’s Current Law – Kirchoff’s Voltage Law • They are the same – but we use COMPLEX NUMBERS.