16- Voltage and Current Dividers, Cicuit Power

Voltage Divider

• Voltage source causes electrons to flow in form of current

• resistors in voltage divider react to force, cause voltage drops

• voltage drop across resistor 2

current divider

• current is flow of electrons

• flow favors the path of least resistance

• current through resistor 2

joules law

• an individual component with resistance R

• a circuit with an equivalent resistance R

Loop current circuit analysis

• select one less than the total number of loops (n-1)

• Assume current directions for teh chosen loops

• Write Kichhoffs volage equation around each loop

• solve for current by using the simultaneous equations generated

superposition theorem

• short all voltages sources, open all current sources, and then turn on only one source at a time

• simplify the circuit to get the current or voltage of interest

• repeat until all source have been used

Thevenins theorem

• Connect an open circuit between terminals A and B. Find V_oc = V_AB, the voltage across the open circuit

• Deactivate the independent sources (replace independent voltage sources with short circuits and independent current sources with open circuits).

• Use circuit analysis to find R_Th. R_Th = R_eq V_Th = V_oc

Norton Equivalent circuit

• Connect a short circuit between terminals A and B. Find I_sc, current from A to B in the short circuit.

• Deactivate the independent sources (replace independent voltage sources with short circuits and independent current sources with open circuits).

• Use circuit analysis to find R_N. R_N = R_eq I_N = I_sc

Maximum Power Transfer Theorem

• A circuit is most efficient when the maximum power available from a source is transfered to a load resistance R_L

• At maximum power transfer, R_L = R_Th

• Page 360

Sinusoid

• Page 360

• Frequency, f, of sinusoid is reciprocal of period T

• Angular Frequency, ω = 2 * π * f

• Instantaneous voltage as a function of time

• V_max is maximum voltage i.e. amplitude of sinusoid

phase shift

• difference between peaks of sinusoids for voltage and current

• due to capacitors and inductors in circuit

phase angle

• magnitude of phase shift

• by convention, voltage taken as reference

Sine/cosine relationship

• a sinusoidal waveform may be represented equally well as either sine or cosine

• The only distinction they hold is that of phase angle π/2 radians