Can the voltage across any of the three components in the R-L-C series circuit ever be larger than the maximum voltage supplied by the AC source? That maximum voltage is 50 volts in this situation. Also, does Kirchoff's loop rule apply to this circuit? In other words, is the sum of the voltages across the resistor, capacitor, and inductor always equal to the source voltage? Select all the true statements from the list below.
1. The voltage across the resistor can exceed the maximum source voltage.
2.
The voltage across the inductor can exceed the maximum source voltage.
3.
The voltage across the capacitor can exceed the maximum source voltage.
4.
None of these voltages can ever exceed the maximum source voltage.
5.
Kirchoff's loop rule is only valid for DC circuits, and does not apply to this AC situation.
6.
Kirchoff's loop rule can be applied to AC circuits, but not to this circuit in particular.
7.
Kirchoff's loop rule is valid for this circuit - at all times the sum of the voltages across the resistor, capacitor, and inductor equal the source voltage.
(b) Resonance is a very special condition in an AC circuit. The resonance frequency is the natural oscillation frequency of the circuit itself, so when the source frequency equals the resonance frequency some special things happen. Select all the statements below that are true at resonance.
8.
For a particular set of R, L, and C values, the current in the circuit is maximized when the circuit is at its resonance frequency.
9.
For a particular set of R, L, and C values, the current in the circuit is minimized when the circuit is at its resonance frequency.
10.
For a particular set of R, L, and C values, the impedance Z of the circuit is maximized when the circuit is at its resonance frequency.
11.
For a particular set of R, L, and C values, the impedance Z of the circuit is minimized when the circuit is at its resonance frequency.
12.
For a particular set of R, L, and C values, the magnitude of the phase angle is zero when the circuit is at its resonance frequency.
13.
For a particular set of R, L, and C values, the magnitude of the phase angle is 90 degrees when the circuit is at its resonance frequency.
14.
For a particular set of R, L, and C values, the power dissipated in the circuit is maximized when the circuit is at its resonance frequency.
15.
For a particular set of R, L, and C values, the power dissipated in the circuit is minimized when the circuit is at its resonance frequency.
1. False. The voltage across the resistor cannot exceed the maximum source voltage. The resistor drops voltage based on the current flowing through it and Ohm's Law (V = I * R).
2. False. The voltage across the inductor cannot exceed the maximum source voltage. The voltage across an inductor is proportional to the rate of change of current through it, and it cannot exceed the applied voltage.
3. False. The voltage across the capacitor cannot exceed the maximum source voltage. The voltage across a capacitor is proportional to the charge stored on it, and it cannot exceed the applied voltage.
4. True. None of these voltages can ever exceed the maximum source voltage.
5. False. Kirchhoff's loop rule is valid for both DC and AC circuits. It states that the sum of the voltage drops in a closed loop equals the sum of the voltage rises. In an AC circuit, the voltage drops can include the voltage drops across resistors, capacitors, and inductors.
6. False. Kirchhoff's loop rule can be applied to this AC circuit. It is a general rule that applies to circuits with any combination of resistors, capacitors, and inductors.
7. True. Kirchhoff's loop rule is valid for this circuit. At all times, the sum of the voltages across the resistor, capacitor, and inductor equals the source voltage.
8. True. For a particular set of R, L, and C values, the current in the circuit is maximized when the circuit is at its resonance frequency.
9. False. For a particular set of R, L, and C values, the current in the circuit is not minimized when the circuit is at its resonance frequency. The minimum current occurs at frequencies far from the resonance frequency.
10. False. For a particular set of R, L, and C values, the impedance Z of the circuit is not maximized when the circuit is at its resonance frequency. The impedance is minimized at resonance.
11. True. For a particular set of R, L, and C values, the impedance Z of the circuit is minimized when the circuit is at its resonance frequency.
12. True. For a particular set of R, L, and C values, the magnitude of the phase angle is zero when the circuit is at its resonance frequency. This means that the voltage and current are in phase at resonance.
13. False. For a particular set of R, L, and C values, the magnitude of the phase angle is not 90 degrees when the circuit is at its resonance frequency. The phase angle is zero at resonance.
14. True. For a particular set of R, L, and C values, the power dissipated in the circuit is maximized when the circuit is at its resonance frequency.
15. False. For a particular set of R, L, and C values, the power dissipated in the circuit is not minimized when the circuit is at its resonance frequency. The minimum power dissipation occurs at frequencies far from the resonance frequency.