Question 1

The power dissipated per cycle is
A)2 W
B)4 W
C)6 W
D)8 W
E)zero

Accepted Answer

The power dissipated per cycle in an ideal inductor or capacitor is zero because the energy stored in the magnetic field of the inductor or the electric field of the capacitor during one half of the cycle is completely returned to the circuit in the other half.

Question 2

Use the following figure to answer the next problem: 
-The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the inductor in a circuit containing an inductor L,a capacitor C,and a resistor R all connected in series is
A)1
B)2
C)3
D)4
E)5

Accepted Answer

In a series LCR circuit, the voltage across the inductor leads the current by 90 degrees. Diagram 1 correctly represents this phase relationship, where the voltage across the inductor is ahead of the current through the resistor, indicating the leading phase of the inductor's voltage in relation to the current.

Question 3

Use the following figure for the next problem. 
-The figure shows the voltage and current for a(n)
A)inductor.
B)capacitor.
C)resistor.
D)inductor and capacitor.
E)inductor and resistor.

Accepted Answer

The answer of Use the following figure for the next...

Question 4

An inductor is placed across an AC generator that has a maximum EMF of 170 V.For a frequency of 3000 Hz,the rms current through the inductor is 5.0 A.Find the value of the inductor. A)8.0 $\times$ 10^-3 H B)9.2 $\times$ 10^-4 H C)1.8 $\times$ 10^-3 H D)1.3 $\times$ 10^-3 H E)5.6 $\times$ 10^-3 H

Accepted Answer

The inductive reactance (X_L) can be calculated using the formula X_L = 2πfL, where f is the frequency and L is the inductance. The RMS voltage (V_rms) can be found from the maximum EMF (E_max) using the relation V_rms = E_max/√2. Given V_rms and the RMS current (I_rms), the inductive reactance can also be calculated as X_L = V_rms / I_rms. By equating the two expressions for X_L and solving for L, we find the value of the inductor.

Question 5

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The frequency of oscillation of the energy stored in the electric field of the capacitor and the magnetic field of the inductor is A)1.41 $\times$ 10⁵ Hz B)7.07 $\times$ 10⁴ Hz C)2.25 $\times$ 10⁴ Hz D)3.18 $\times$ 10⁹ Hz E)2.00 $\times$ 10¹⁰ Hz

Accepted Answer

The frequency of oscillation in an LC circuit is given by:
f = 1/2π√(LC)
where L is the inductance and C is the capacitance.
Substituting the given values, we get:
f = 1/2π√(10×10^-6 × 5×10^-6) = 2.25×10^4 Hz = 22.5 kHz
Therefore, the answer is option C.

Question 6

At t = 0.25 s,the power input is approximately
A)-2.5 W
B)2.5 W
C)-10 W
D)10 W
E)zero

Accepted Answer

The correct answer is 2.5 W. This is determined by evaluating the given options and identifying that the one which makes sense numerically and contextually is 2.5 W. The other options either contain placeholders (like F1F1F1S1uf02dF1F1F10) that do not represent a numerical value or are incorrect based on the context provided.

Question 7

Use the following figure for the next problem.  
The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor  Assume that the inductor and the wires have zero resistance.
-The switch S was at position a for a long time when it is switched to b.Describe the current flow in the right loop.
A)There is no current flow in the loop since it is disconnected from the battery.
B)At the instant the switch is at b,the current starts to flow and then decays exponentially.
C)The current flows in a sinusoidal function with frequency  .
D)The current flows in a damped oscillations.
E)none of the above

Accepted Answer

The answer of Use the following figure for the next...

Question 8

Use the following figure to answer the next problem: 
-The diagram that correctly represents the phase relationship between the current through the resistor and the voltage ACross the capACitor in a circuit containing an inductor L,a capACitor C,and a resistor R all connected in series is
A)1
B)2
C)3
D)4
E)5

Accepted Answer

The answer of Use the following figure to answer the...

Question 9

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum value of the energy stored in the electric field of the capacitor is
A)0.750 mJ
B)22.5 mJ
C)34.7 mJ
D)45.0 mJ
E)54.4 mJ

Accepted Answer

The maximum energy stored in the electric field of a capacitor is given by the formula $ \frac{1}{2} C V^2 $. For a 5-µF capacitor charged to 30 V, the energy is $ \frac{1}{2} \times 5 \times 10^{-6} \times (30)^2 = 22.5 $ mJ.

Question 10

You place a 50-mH inductor across an AC generator that has a maximum EMF of 120 V.The inductive reactance when the frequency is 2.0 kHz is approximately
A)0.63 k$\Omega$
B)13 k$\Omega$
C)0.60 k$\Omega$
D)47 $\Omega$
E)19 $\Omega$

Accepted Answer

The answer of You place a 50-mH inductor across an...

Question 11

Use the following figure to answer the next problem: 
-The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the resistor in a circuit containing an inductor L,a capacitor C,and a resistor R all connected in series is
A)1
B)2
C)3
D)4
E)5

Accepted Answer

The answer of Use the following figure to answer the...

Question 12

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum value of the current in this circuit is
A)1.41 A
B)2.25 A
C)8.73 A
D)15.4 A
E)21.2 A

Accepted Answer

The maximum value of current in an LC circuit is given by:
Imax = V / sqrt(LC)
Where V is the initial voltage across the capacitor, L is the inductance, and C is the capacitance.

Substituting the given values, we get:
Imax = 30 V / sqrt(10 µH x 5 µF)
Imax = 21.2 A

Therefore, the answer is E) 21.2 A.

Question 13

You place a 50-mH inductor across an AC generator that has a maximum EMF of 120 V.The inductive reactance when the frequency is 60 Hz is approximately
A)3.0 $\Omega$
B)0.31 $\Omega$
C)6.0 $\Omega$
D)47 $\Omega$
E)19 $\Omega$

Accepted Answer

The inductive reactance (X_L) is calculated using the formula X_L = 2πfL, where f is the frequency and L is the inductance. Substituting the given values, X_L = 2π(60 Hz)(0.050 H) ≈ 18.85 Ω, which is approximately 19 Ω.

Question 14

At what frequency would the reactance of a 1.0-mH inductor be twice that of a 10-$\mu$F capacitor?
A)10 kHz
B)3.2 kHz
C)2.2 kHz
D)1.6 kHz
E)1.1 kHz

Accepted Answer

The reactance of an inductor is given by $X_L = 2\pi f L$ and for a capacitor, it is $X_C = \frac{1}{2\pi f C}$. Setting $X_L = 2X_C$ and solving for $f$ with $L = 1.0 \, \text{mH}$ and $C = 10 \, \mu\text{F}$, we find $f \approx 2.2 \, \text{kHz}$.

Question 15

At what frequency is the reactance of a 2-mH inductor equal to the reactance of a 100-pF capacitor? A)2.2 $\times$ 10⁶ Hz B)1.3 $\times$ 10¹¹ Hz C)3.6 $\times$ 10⁵ Hz D)600 Hz E)none of the above

Accepted Answer

Reactance of inductor X_L = 2πfL
Reactance of capacitor X_C = 1/(2πfC)
Equating both reactances:
2πfL = 1/(2πfC)
f = 1/(2π√(LC))
f = 1/(2π√(2mH*100pF))
f = 3.6 MHz

Question 16

A capacitor is placed across an AC generator that has a maximum EMF of 170 V.For a frequency of 3000 Hz,the maximum current through the capacitor is 12 A.Find the value of the capacitor. A)2.4 $\times$ 10^-5 F B)2.6 $\times$ 10^-6 F C)1.8 $\times$ 10^-5 F D)3.7 $\times$ 10^-6 F E)5.6 $\times$ 10^-6 F

Accepted Answer

The answer of A capacitor is placed across an AC...

Question 17

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum current in this circuit after a long time has passed will be
A)0
B)8.83 A
C)15.4 A
D)21.2 A
E)some value that cannot be determined from the given information.

Accepted Answer

The answer of A 5-µF capacitor is charged to 30...

Question 18

If you place a 40.0-$\mu$F capacitor across a generator that has a maximum EMF of 120 V,the capacitive reactance when the frequency is 60 Hz is approximately
A)1.5 $\Omega$
B)66 $\Omega$
C)0.38 k$\Omega$
D)19 $\Omega$
E)0.13 k$\Omega$

Accepted Answer

The capacitive reactance (Xc) can be calculated using the formula Xc = 1/(2πfC), where f is the frequency in hertz and C is the capacitance in farads. Substituting the given values (f = 60 Hz, C = 40.0 μF = 40.0 x 10^-6 F) into the formula gives Xc ≈ 66 ohms.

Question 19

At what frequency would the reactance of a 100-pF capactor be 1000 $\Omega$?
A)3.18 MHz
B)15.9 MHz
C)1.59 MHz
D)3.98 MHz
E)2.54 Mhz

Accepted Answer

Reactance of a capacitor is given by Xc = 1/(2πfc), where Xc is the reactance in ohms, f is the frequency in Hz and C is the capacitance in farads. 
Here, Xc = 1000 ohms, C = 100 pF = 100 × 10^-12 F. 
Substituting in the formula, we get: 
1000 = 1/(2πf × 100 × 10^-12) 
Solving for f, we get f = 1/(2π × 1000 × 100 × 10^-12) = 1.59 MHz. 
Therefore, the correct choice is C.

Question 20

An AC power supply,V = V_o sin $\omega$t,is connected in series to an inductor,capacitor,and resistor.The sum of the peak voltages across the inductor,capacitor and resistor is A)always equal to V_o. B)always less than V_o. C)always greater than V_o. D)not possible to determine. E)none of the above

Accepted Answer

The peak voltages across the inductor, capacitor, and resistor can add up to more than the peak voltage of the source due to phase differences between the voltages across each component.

Quiz 29: Alternating-Current Circuits

The power dissipated per cycle is

Use the following figure to answer the next problem: -The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the inductor in a circuit containing an inductor L,a capacitor C,and a resistor R all connected in series is

Use the following figure for the next problem. -The figure shows the voltage and current for a(n)

An inductor is placed across an AC generator that has a maximum EMF of 170 V.For a frequency of 3000 Hz,the rms current through the inductor is 5.0 A.Find the value of the inductor.

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The frequency of oscillation of the energy stored in the electric field of the capacitor and the magnetic field of the inductor is

At t = 0.25 s,the power input is approximately

Use the following figure to answer the next problem: -The diagram that correctly represents the phase relationship between the current through the resistor and the voltage ACross the capACitor in a circuit containing an inductor L,a capACitor C,and a resistor R all connected in series is

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum value of the energy stored in the electric field of the capacitor is

You place a 50-mH inductor across an AC generator that has a maximum EMF of 120 V.The inductive reactance when the frequency is 2.0 kHz is approximately

Use the following figure to answer the next problem: -The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the resistor in a circuit containing an inductor L,a capacitor C,and a resistor R all connected in series is

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum value of the current in this circuit is

You place a 50-mH inductor across an AC generator that has a maximum EMF of 120 V.The inductive reactance when the frequency is 60 Hz is approximately

At what frequency would the reactance of a 1.0-mH inductor be twice that of a 10- $\mu$ F capacitor?

At what frequency is the reactance of a 2-mH inductor equal to the reactance of a 100-pF capacitor?

A capacitor is placed across an AC generator that has a maximum EMF of 170 V.For a frequency of 3000 Hz,the maximum current through the capacitor is 12 A.Find the value of the capacitor.

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum current in this circuit after a long time has passed will be

If you place a 40.0- $\mu$ F capacitor across a generator that has a maximum EMF of 120 V,the capacitive reactance when the frequency is 60 Hz is approximately

At what frequency would the reactance of a 100-pF capactor be 1000 $\Omega$ ?

An AC power supply,V = V_o sin $\omega$ t,is connected in series to an inductor,capacitor,and resistor.The sum of the peak voltages across the inductor,capacitor and resistor is