به انگلیسی

Phasors: adding AC voltages with different phases

Science · Electricity & Magnetism · ages 20-21

Name ______________________ Date ____________

What is the inductive reactance XL of an ideal inductor at angular frequency omega?
- 1 over omega C
- R times omega
- omega times L
For an ideal capacitor in sinusoidal steady state, how do current and voltage line up?
- Current leads voltage by a quarter cycle
- Current lags voltage by a quarter cycle
- Current and voltage peak at the same time
In an ideal series RLC phasor diagram, the resistor voltage arrow points in the same direction as the current arrow.
Circle one: True False
An ideal series RLC circuit with R > 0 is driven below resonance. How does current line up with supply voltage?
- Current lags
- They stay in step
- Current leads
An ideal series RLC circuit has R = 3 ohm, XL = 7 ohm and Xc = 3 ohm. What is its impedance magnitude Z?
- 13 ohm
- 5 ohm
- 4 ohm
A sinusoidal supply of voltage amplitude 15 V drives a circuit with impedance magnitude Z = 5 ohm. What is the current amplitude?
- 3 A
- 75 A
- 0.33 A
A series RLC circuit has R = 4 ohm, XL = 9 ohm and Xc = 5 ohm. What is phi, defined as supply voltage phase minus current phase?
- 45 degrees; current leads voltage
- 0 degrees; current stays in phase
- 45 degrees; current lags voltage
In a series RLC circuit, voltage amplitudes are VR = 5 V, VL = 15 V and VC = 3 V. Sam adds all three and gets 23 V. What is the supply voltage amplitude?
- 23 V, from adding all peaks
- 13 V, from the phasor sum
- 12 V, from cancelling R too

Answer key

For grown-ups. Fold this page away before handing over the rest.

omega times L · Inductive reactance is XL = omega L, measured in ohms.
Current leads voltage by a quarter cycle · The current reaches its positive peak a quarter cycle before the capacitor voltage reaches its positive peak.
True · Resistor voltage and current are in phase, so their phasors point in the same direction.
Current leads · Below resonance Xc > XL. The net reactance is capacitive, so current leads supply voltage.
5 ohm · The net reactance is 7 - 3 = 4 ohm. Z = sqrt(3^2 + 4^2) = 5 ohm.
3 A · I0 = V0/Z = 15/5 = 3 A. Both voltage and current are amplitudes.
45 degrees; current lags voltage · tan phi = (9 - 5)/4 = 1, so phi = 45 degrees. Positive phi means current lags supply voltage.
13 V, from the phasor sum · VL and VC oppose, giving 12 V. Combine that with VR: V0 = sqrt(5^2 + 12^2) = 13 V. Adding the positive amplitudes gives Sam's 23 V.