For a series ac R-L-C circuit, (a) why do the voltage amplitudes not obey the equation V = V R + V L + V C ; and (b) would the instantaneous voltages obey the equation U = U R + U L + U C ? Why or why not?

Question

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Answer 1

Textbook Question

Chapter 22, Problem 1CQ

For a series ac R-L-C circuit, (a) why do the voltage amplitudes not obey the equation V = V_R + V_L + V_C; and (b) would the instantaneous voltages obey the equation U = U_R+ U_L + U_C? Why or why not?

(a)

Expert Solution

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

(b)

Expert Solution

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule

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Answer 2

Textbook Question

Chapter 22, Problem 1CQ

For a series ac R-L-C circuit, (a) why do the voltage amplitudes not obey the equation V = V_R + V_L + V_C; and (b) would the instantaneous voltages obey the equation U = U_R+ U_L + U_C? Why or why not?

(a)

Expert Solution

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

(b)

Expert Solution

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule

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Answer 3

Textbook Question

Chapter 22, Problem 1CQ

For a series ac R-L-C circuit, (a) why do the voltage amplitudes not obey the equation V = V_R + V_L + V_C; and (b) would the instantaneous voltages obey the equation U = U_R+ U_L + U_C? Why or why not?

(a)

Expert Solution

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

(b)

Expert Solution

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule

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Answer 4

Textbook Question

Chapter 22, Problem 1CQ

For a series ac R-L-C circuit, (a) why do the voltage amplitudes not obey the equation V = V_R + V_L + V_C; and (b) would the instantaneous voltages obey the equation U = U_R+ U_L + U_C? Why or why not?

(a)

Expert Solution

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

(b)

Expert Solution

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

(b)

Expert Solution

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule

Answer 8

(a)

Expert Solution

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The reason for which the voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC.

Answer 13

Answer to Problem 1CQ

The voltage amplitude in a series R−L−C circuit do not follow the equation V=VR+VL+VC since the individual voltages achieve their maximum values at different times.

Answer 14

Explanation of Solution

A series R−L−C circuit is an oscillating circuit. The current and voltage in the circuit oscillates in time with maintaining phase difference between them. Moreover, there exist phase difference in voltage across the inductor and that across the capacitor.

Since there exist phase difference between the voltages across the components resistor, inductor, and capacitor, the maximum value of the voltages across different components will present at different time. This makes the direct addition of the voltages across the components do not give the maximum voltage amplitude.

Answer 15

(b)

Expert Solution

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Whether the instantaneous voltages in the series R−L−C circuit obey the equation U=UR+UL+UC or not.

Answer 20

Answer to Problem 1CQ

The instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule.

Answer 21

Explanation of Solution

According to the Kirchhoff’s loop rule, the algebraic sum of all voltages in a loop must be zero. In other words, the net voltage in a loop will be zero. Applying the Kirchhoff’s loop rule to a series R−L−C circuit, at any instant the total potential difference across the circuit will be equal to the sum of the individual voltages across the three components.

The Kirchhoff’s loop rule is agreed by the series R−L−C circuit when the instantaneous voltages obey the equation U=UR+UL+UC. Here, the sum of the instantaneous voltages will not be the peak voltage amplitude of the circuit. Therefore, the instantaneous voltages in the series R−L−C circuit obeys the equation U=UR+UL+UC in accordance with the Kirchhoff’s loop rule