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.
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The correct answers are:
1. The voltage across the resistor can exceed the maximum source voltage.
4. None of these voltages can ever exceed the maximum source voltage.
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.
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.
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.
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.
1. The voltage across the resistor can exceed the maximum source voltage.
Explanation: In a series circuit, the voltage across each component depends on its resistance, reactance, and the current flowing through it. Depending on the values of these parameters, the voltage across the resistor can exceed the maximum source voltage.
2. The voltage across the inductor can exceed the maximum source voltage.
Explanation: Similar to the resistor, the voltage across the inductor can also exceed the maximum source voltage due to the reactance of the inductor and the current flowing through it.
3. The voltage across the capacitor can exceed the maximum source voltage.
Explanation: Like the other components, the voltage across the capacitor can also exceed the maximum source voltage depending on its reactance and the current flowing through it.
4. None of these voltages can ever exceed the maximum source voltage.
Explanation: This statement is false, as explained in statements 1, 2, and 3.
5. Kirchoff's loop rule is only valid for DC circuits and does not apply to this AC situation.
Explanation: This statement is false. Kirchoff's loop rule is applicable to both DC and AC circuits. It states that the sum of the voltages around any closed loop in a circuit is zero.
6. Kirchoff's loop rule can be applied to AC circuits but not to this circuit in particular.
Explanation: This statement is false. Kirchoff's loop rule can be applied to this AC circuit, just like any other circuit.
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.
Explanation: This statement is true. Kirchoff's loop rule is valid for this circuit, and the sum of the voltages across the resistor, capacitor, and inductor will always equal the source voltage in a series circuit.
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.
Explanation: This statement is true. At resonance, the impedance of the circuit is minimized, allowing maximum current to flow through the circuit.
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.
Explanation: This statement is false. At resonance, the current in the circuit is maximized, not minimized.
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.
Explanation: This statement is false. At resonance, the impedance of the circuit is minimized, not maximized.
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.
Explanation: This statement is true. At resonance, the impedance of the circuit is minimized, allowing maximum current to flow.
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.
Explanation: This statement is true. At resonance, the phase angle between the voltage and current is zero degrees.
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.
Explanation: This statement is false. At resonance, the phase angle between the voltage and current is zero degrees, not 90 degrees.
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.
Explanation: This statement is false. At resonance, the power factor is unity, which means the power dissipated in the circuit is maximized. However, the power factor is not the same as power dissipation.
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.
Explanation: This statement is true. At resonance, the power factor is unity, resulting in minimal power losses. Therefore, the power dissipated in the circuit is minimized.