A series RLC circuit can have a higher voltage than the source voltage across the resistor.

Question

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Answer 1

Textbook Question

Chapter 13, Problem 1TFQ

A series RLC circuit can have a higher voltage than the source voltage across the resistor.

Expert Solution & Answer

To determine

Whether the given statement is true or false.

Answer to Problem 1TFQ

False.

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

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Answer 2

Textbook Question

Chapter 13, Problem 1TFQ

A series RLC circuit can have a higher voltage than the source voltage across the resistor.

Expert Solution & Answer

To determine

Whether the given statement is true or false.

Answer to Problem 1TFQ

False.

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

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Answer 3

Textbook Question

Chapter 13, Problem 1TFQ

A series RLC circuit can have a higher voltage than the source voltage across the resistor.

Expert Solution & Answer

To determine

Whether the given statement is true or false.

Answer to Problem 1TFQ

False.

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

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Answer 4

Textbook Question

Chapter 13, Problem 1TFQ

A series RLC circuit can have a higher voltage than the source voltage across the resistor.

Expert Solution & Answer

To determine

Whether the given statement is true or false.

Answer to Problem 1TFQ

False.

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Whether the given statement is true or false.

Answer to Problem 1TFQ

False.

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

Answer 8

Expert Solution & Answer

To determine

Whether the given statement is true or false.

Answer to Problem 1TFQ

False.

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Whether the given statement is true or false.

Answer 12

Answer to Problem 1TFQ

False.

Answer 13

Explanation of Solution

Given:

The given statement is:

The voltage across the resistor in a series RLC circuit is higher than the source voltage.

Calculation:

In case of a series resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. This means that for the current brought up through any one branch, the other branch needs to return it to the ground at the same rate. That is, the currents through those branches must cancel out each other to zero.That is why, the value of total current in the L and C branches of a parallel circuit at resonance will be zero.

When the frequency is less than the resonant frequency, the value of inductive reactance is less than the capacitive reactance. In case of the parallel circuits, the current in the branch having more reactance will be less than the branch having less reactance. This concludes that the current flowing through the inductor is more and hence, the circuit is an inductive circuit. Current lags the voltage in case of inductive circuits.

In case of a parallel resonant circuit, the capacitive reactance and the inductive reactance are equal and opposite to each other. Therefore, they cancel out each other’s effect. That is, the current in the capacitive branch and the inductive branch are always 180 degrees out of phase to each other. Therefore, the capacitive and the inductive current subtract from each other.That is, the remaining circuit behaves like a resistive circuit. Hence, the voltage across the resistor is equal to the source voltage. The total current in the circuit will be equal to the resistance current.

Therefore, the given statement is False.

Answer 14

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A series RLC circuit can have a higher voltage than the source voltage across the resistor.

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Answer to Problem 1TFQ

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