
E5A01 What can cause the voltage across reactances in series to be larger than the voltage applied to them?
A. Resonance
B. Capacitance
C. Conductance
D. Resistance
 (A)
 At resonance, the voltage across the inductor and capacitor in a series circuit can be many times greater than the applied voltage. In practical circuits, it can be 10 or 100 times greater. How can this be? The reason is that the capacitor and inductor store the supplied energy, dissipating a small amount of it in resistive losses. The applied voltage “pumps” the resonant circuit, building up energy in each component.

E5A02 What is resonance in an electrical circuit?
A. The highest frequency that will pass current
B. The lowest frequency that will pass current
C. The frequency at which the capacitive reactance equals the inductive reactance
D. The frequency at which the reactive impedance equals the resistive impedance
 (C)
 At resonance, capacitive and inductive reactance in a circuit are equal.

E5A03 What is the magnitude of the impedance of a series RLC circuit at resonance?
A. High, as compared to the circuit resistance
B. Approximately equal to capacitive reactance
C. Approximately equal to inductive reactance
D. Approximately equal to circuit resistance
 (D)
 In a series circuit at resonance, the inductive reactance of L and the capacitive reactance of C cancel, leaving only the circuit resistance.

E5A04 What is the magnitude of the impedance of a circuit with a resistor, an inductor and a capacitor all in parallel, at resonance?
A. Approximately equal to circuit resistance
B. Approximately equal to inductive reactance
C. Low, as compared to the circuit resistance
D. Approximately equal to capacitive reactance
 (A)
 In a parallel circuit the basic principle of resonance is the same as for series circuits: the inductive reactance of L and the capacitive reactance of C cancel so all that remains is the circuit resistance.

E5A05 What is the magnitude of the current at the input of a series RLC circuit as the frequency goes through resonance?
A. Minimum
B. Maximum
C. R/L
D. L/R
 (B)
 Current in a series circuit is maximum at resonance because the inductive and capacitive reactances cancel.

E5A06 What is the magnitude of the circulating current within the components of a parallel LC circuit at resonance?
A. It is at a minimum
B. It is at a maximum
C. It equals 1 divided by the quantity 2 times Pi, multiplied by the square root of inductance L multiplied by capacitance C
D. It equals 2 multiplied by Pi, multiplied by frequency "F", multiplied by inductance "L"
 (B)
 The circulating current within the components of a parallel LC circuit are maximum at resonance. Circulating current transfers the circuit’s stored energy back and forth between the inductive and capacitive reactance. When the two types of reactance are equal or balanced at resonance, the circulating current is at a maximum even though net current through the entire circuit is at a minimum.

E5A07 What is the magnitude of the current at the input of a parallel RLC circuit at resonance?
A. Minimum
B. Maximum
C. R/L
D. L/R
 (A)
 At resonance, the circulating current of a parallel circuit is out of phase with the applied current. The effect is that very little net current flows through the resonant circuit and its impedance is very high. Current in a parallel RLC circuit does not go to zero at resonance because of the remaining resistance.

E5A08 What is the phase relationship between the current through and the voltage across a series resonant circuit at resonance?
A. The voltage leads the current by 90 degrees
B. The current leads the voltage by 90 degrees
C. The voltage and current are in phase
D. The voltage and current are 180 degrees out of phase
(C)

E5A09 What is the phase relationship between the current through and the voltage across a parallel resonant circuit at resonance?
A. The voltage leads the current by 90 degrees
B. The current leads the voltage by 90 degrees
C. The voltage and current are in phase
D. The voltage and current are 180 degrees out of phase
 (C)
 At resonance, the impedance of the circuit is completely resistive because the inductive and capacitive reactances have cancelled. In a resistive circuit, voltage and current are always in phase.

E5A10 What is the halfpower bandwidth of a parallel resonant circuit that has a resonant frequency of 1.8 MHz and a Q of 95?
A. 18.9 kHz
B. 1.89 kHz
C. 94.5 kHz
D. 9.45 kHz
 (A)
 The relationship between bandwidth, BW, resonant frequency, f0, and quality factor, Q, is:

E5A11 What is the halfpower bandwidth of a parallel resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150?
A. 157.8 Hz
B. 315.6 Hz
C. 47.3 kHz
D. 23.67 kHz
 (C)

E5A12 What is the halfpower bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118?
A. 436.6 kHz
B. 218.3 kHz
C. 31.4 kHz
D. 15.7 kHz
 (C)

E5A13 What is the halfpower bandwidth of a parallel resonant circuit that has a resonant frequency of 14.25 MHz and a Q of 187?
A. 38.1 kHz
B. 76.2 kHz
C. 1.332 kHz
D. 2.665 kHz
 (B)

E5A14 What is the resonant frequency of a series RLC circuit if R is 22 ohms, L is 50 microhenrys and C is 40 picofarads?
A. 44.72 MHz
B. 22.36 MHz
C. 3.56 MHz
D. 1.78 MHz
 (C)

E5A15 What is the resonant frequency of a series RLC circuit if R is 56 ohms, L is 40 microhenrys and C is 200 picofarads?
A. 3.76 MHz
B. 1.78 MHz
C. 11.18 MHz
D. 22.36 MHz
 (B)

E5A16 What is the resonant frequency of a parallel RLC circuit if R is 33 ohms, L is 50 microhenrys and C is 10 picofarads?
A. 23.5 MHz
B. 23.5 kHz
C. 7.12 kHz
D. 7.12 MHz
 (D)

E5A17 What is the resonant frequency of a parallel RLC circuit if R is 47 ohms, L is 25 microhenrys and C is 10 picofarads?
A. 10.1 MHz
B. 63.2 MHz
C. 10.1 kHz
D. 63.2 kHz
 (A)

E5B01 What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the applied voltage?
A. An exponential rate of one
B. One time constant
C. One exponential period
D. A time factor of one
 (B)
 In an RC circuit, when the capacitor has no initial charge, it takes one time constant to charge the capacitor to 63.2% of the applied voltage. In the graph, you can see how the voltage across a capacitor rises with time, when charged through a resistor. The graphs show voltage across a capacitor as it charges (A) and discharges (B) through a resistor.

E5B02 What is the term for the time it takes for a charged capacitor in an RC circuit to discharge to 36.8% of its initial voltage?
A. One discharge period
B. An exponential discharge rate of one
C. A discharge factor of one
D. One time constant
 (D)
 The voltage while charging and discharging has the same general exponential shape, so it takes one time constant to discharge 63.2% of the initial voltage, which leaves 36.8% of the initial voltage across the capacitor.

E5B03 The capacitor in an RC circuit is discharged to what percentage of the starting voltage after two time constants?
A. 86.5%
B. 63.2%
C. 36.8%
D. 13.5%
 (D)
 The voltage after discharging for one time constant can be treated as the initial voltage for the second time constant. The voltage remaining after two time constants, then, is 36.8% of 36.8% = 13.5%. The discharge graph shows the result

E5B04 What is the time constant of a circuit having two 220microfarad capacitors and two 1megohm resistors, all in parallel?
A. 55 seconds
B. 110 seconds
C. 440 seconds
D. 220 seconds
 (D)
 In this parallel circuit, the total resistance is 500 kW. The total capacitance is 440 µF. The time constant is:
 t = R C = (500 x 10^{3}) x (440 x 10^{6}) = 220 seconds

E5B05 How long does it take for an initial charge of 20 V DC to decrease to 7.36 V DC in a 0.01microfarad capacitor when a 2megohm resistor is connected across it?
A. 0.02 seconds
B. 0.04 seconds
C. 20 seconds
D. 40 seconds
 (A)
 Find out how many time constants this amount of discharge represents. Because 7.36 V is 36.8% of 20 V (7.36/20), the circuit has discharged for one time constant as you can see on the discharge curve. The time constant for this circuit is:
t = R C = (2 x 106) x (0.01 x 106) = 0.02 seconds

E5B06 How long does it take for an initial charge of 800 V DC to decrease to 294 V DC in a 450microfarad capacitor when a 1megohm resistor is connected across it?
A. 4.50 seconds
B. 9 seconds
C. 450 seconds
D. 900 seconds
 (C)
 Find out how many time constants the discharge represents. 294 V is 36.8% of 800 V so the circuit has discharged by one time constant. The time constant for the circuit is:
t = R C = (1 x 10^{6}) x (450 x 10^{6}) = 450 seconds

E5B07 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms?
A. 68.2 degrees with the voltage leading the current
B. 14.0 degrees with the voltage leading the current
C. 14.0 degrees with the voltage lagging the current
D. 68.2 degrees with the voltage lagging the current
 (C)
 You should be familiar with polar coordinates to answer this question. The total reactance in this series configuration is 250 Ω – 500 Ω = –250 Ω. The phase angle between the voltage and the current is:
 Because the angle is negative, the voltage lags the current. Since the net reactance is negative, the phase angle needs to be negative. Because the net reactance is smaller than the resistance, the phase angle will be less than 45°.

E5B08 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 100 ohms, R is 100 ohms, and XL is 75 ohms?
A. 14 degrees with the voltage lagging the current
B. 14 degrees with the voltage leading the current
C. 76 degrees with the voltage leading the current
D. 76 degrees with the voltage lagging the current
 (A)
 The total reactance in this series configuration is 75 Ω – 100 Ω. The phase angle between the voltage and the current is:
 Voltage lags current because the phase angle is negative.

E5B09 What is the relationship between the current through a capacitor and the voltage across a capacitor?
A. Voltage and current are in phase
B. Voltage and current are 180 degrees out of phase
C. Voltage leads current by 90 degrees
D. Current leads voltage by 90 degrees
 (D)
 For a capacitor, the current leads voltage by 90°. Use the mnemonic “Eli the iceman”  it’s an easy way to remember current and voltage relationships in reactive circuits. ELI means voltage (E) leads current (I) in an inductance (L) and ICE means current (I) leads voltage (E) in a capacitor (C). For a pure reactance (no resistance), the phase angle is 90°.

E5B10 What is the relationship between the current through an inductor and the voltage across an inductor?
A. Voltage leads current by 90 degrees
B. Current leads voltage by 90 degrees
C. Voltage and current are 180 degrees out of phase
D. Voltage and current are in phase
 (A)
 For an inductor, the voltage leads current by 90°. Use the mnemonic “Eli the iceman”  it’s an easy way to remember current and voltage relationships in reactive circuits. ELI means voltage (E) leads current (I) in an inductance (L) and ICE means current (I) leads voltage (E) in a capacitor (C). For a pure reactance (no resistance), the phase angle is 90°.

E5B11 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 50 ohms?
A. 14 degrees with the voltage lagging the current
B. 14 degrees with the voltage leading the current
C. 76 degrees with the voltage lagging the current
D. 76 degrees with the voltage leading the current
 (B)
 The total reactance in this series configuration is 50 Ω – 25 Ω. The phase angle between the voltage and the current is:
 The positive angle means that voltage leads current. A rule of thumb is that since the net reactance is positive, the phase angle needs to be positive; because the net reactance is smaller than the resistance, the phase angle needs to be less than 45°.

E5B12 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 75 ohms, R is 100 ohms, and XL is 50 ohms?
A. 76 degrees with the voltage lagging the current
B. 14 degrees with the voltage leading the current
C. 14 degrees with the voltage lagging the current
D. 76 degrees with the voltage leading the current
 (C)
 The total reactance in this series configuration is 50 Ω – 75 Ω. The phase angle between the voltage and the current is:
 A negative phase angle means that voltage lags current. A rule of thumb is that since the net reactance is negative, the phase angle needs to be negative; because the net reactance is smaller than the resistance, the phase angle needs to be less than 45°.

E5B13 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 250 ohms, R is 1 kilohm, and XL is 500 ohms?
A. 81.47 degrees with the voltage lagging the current
B. 81.47 degrees with the voltage leading the current
C. 14.04 degrees with the voltage lagging the current
D. 14.04 degrees with the voltage leading the current
 (D)
 The total reactance in this series configuration is 500 Ω – 250 Ω. The phase angle between the voltage and the current is:
 The positive angle means that voltage leads current. A rule of thumb is that since the net reactance is positive, the phase angle needs to be positive; because the net reactance is smaller than the resistance, the phase angle needs to be less than 45°.

E5C01 In polar coordinates, what is the impedance of a network consisting of a 100ohmreactance inductor in series with a 100ohm resistor?
A. 121 ohms at an angle of 35 degrees
B. 141 ohms at an angle of 45 degrees
C. 161 ohms at an angle of 55 degrees
D. 181 ohms at an angle of 65 degrees
 (B)
 In rectangular coordinates, impedance is the sum of the resistive and reactive components. You plot impedance with resistance on the X axis and reactance on the Y axis. In polar coordinates, impedance is described by magnitude and the corresponding phase angle. You can calculate these from resistance (R) and reactance (X) using the following formulas, in which the vertical bars around Z indicate “magnitude” without regard to the phase angle.

E5C02 In polar coordinates, what is the impedance of a network consisting of a 100ohmreactance inductor, a 100ohmreactance capacitor, and a 100ohm resistor, all connected in series?
A. 100 ohms at an angle of 90 degrees
B. 10 ohms at an angle of 0 degrees
C. 10 ohms at an angle of 90 degrees
D. 100 ohms at an angle of 0 degrees
 (D)
 This is a resonant circuit because the capacitive and inductive reactances are equal. That means that the reactances cancel and you have only the resistance left, which is an impedance of 100 ohms with no reactive phase shift (angle = 0°).

E5C03 In polar coordinates, what is the impedance of a network consisting of a 300ohmreactance capacitor, a 600ohmreactance inductor, and a 400ohm resistor, all connected in series?
A. 500 ohms at an angle of 37 degrees
B. 900 ohms at an angle of 53 degrees
C. 400 ohms at an angle of 0 degrees
D. 1300 ohms at an angle of 180 degrees
 (A)
 Capacitive reactance is negative so the net reactance is 600 Ω  300 Ω = 300 Ω. Use the formulas for converting to polar coordinates and find:

E5C04 In polar coordinates, what is the impedance of a network consisting of a 400ohmreactance capacitor in series with a 300ohm resistor?
A. 240 ohms at an angle of 36.9 degrees
B. 240 ohms at an angle of 36.9 degrees
C. 500 ohms at an angle of 53.1 degrees
D. 500 ohms at an angle of 53.1 degrees
 (D)
 Use the formulas for converting to polar coordinates and find:

E5C05 In polar coordinates, what is the impedance of a network consisting of a 400ohmreactance inductor in parallel with a 300ohm resistor?
A. 240 ohms at an angle of 36.9 degrees
B. 240 ohms at an angle of 36.9 degrees
C. 500 ohms at an angle of 53.1 degrees
D. 500 ohms at an angle of 53.1 degrees
 (A)

E5C06 In polar coordinates, what is the impedance of a network consisting of a 100ohmreactance capacitor in series with a 100ohm resistor?
A. 121 ohms at an angle of 25 degrees
B. 191 ohms at an angle of 85 degrees
C. 161 ohms at an angle of 65 degrees
D. 141 ohms at an angle of 45 degrees
 (D)

E5C07 In polar coordinates, what is the impedance of a network comprised of a 100ohmreactance capacitor in parallel with a 100ohm resistor?
A. 31 ohms at an angle of 15 degrees
B. 51 ohms at an angle of 25 degrees
C. 71 ohms at an angle of 45 degrees
D. 91 ohms at an angle of 65 degrees
 (C)

E5C08 In polar coordinates, what is the impedance of a network comprised of a 300ohmreactance inductor in series with a 400ohm resistor?
A. 400 ohms at an angle of 27 degrees
B. 500 ohms at an angle of 37 degrees
C. 500 ohms at an angle of 47 degrees
D. 700 ohms at an angle of 57 degrees
 (B)

E5C09 When using rectangular coordinates to graph the impedance of a circuit, what does the horizontal axis represent?
A. Resistive component
B. Reactive component
C. The sum of the reactive and resistive components
D. The difference between the resistive and reactive components
 (A)
 The horizontal axis represents the resistive component.

E5C10 When using rectangular coordinates to graph the impedance of a circuit, what does the vertical axis represent?
A. Resistive component
B. Reactive component
C. The sum of the reactive and resistive components
D. The difference between the resistive and reactive components
 (B)
 The vertical axis represents the reactive component.

