Question 1

A 3.00-$\mu$F capacitor was fully charged by being connected to a 9.00-V battery.The fully charged capacitor is then connected to a 0.500-H inductor.The frequency of oscillation of the LC circuit is
A)130 Hz.
B)15.2 Hz.
C)1.89 Hz.
D)22.7 Hz.
E)356 Hz

Accepted Answer

The frequency of oscillation for an LC circuit is given by $ f = \frac{1}{2\pi\sqrt{LC}} $. Substituting $ L = 0.500 \, \text{H} $ and $ C = 3.00 \times 10^{-6} \, \text{F} $, we find $ f \approx 130 \, \text{Hz} $.

Question 2

At what frequency will a 20 mH inductor have a reactance X_L = 500 $\varOmega$ ? A)62.8 Hz B)3980 Hz C)2210 Hz D)125 Hz E)8120 Hz

Accepted Answer

Reactance of an inductor is given by:
XL = 2πfL
Where XL is the reactance of the inductor, f is the frequency in Hertz, and L is the inductance in Henrys.

Given: L = 20 mH = 0.02 H, XL = 500 Ω.

Substituting these values in the above equation, we get:

500 = 2πf(0.02)
f = 500 / (2π × 0.02) = 3980 Hz

Therefore, the answer is B) 3980 Hz.

Question 3

At what frequency will a 20-µF capacitor have a reactance X_C = 500 $\varOmega$ ? A)51 Hz B)42 Hz C)35 Hz D)27 Hz E)16 Hz

Accepted Answer

E

Question 4

The total amount of energy stored in an LC series circuit is 8.00 J.When the current through the inductor is equal to half its maximum value,how much energy is stored in the magnetic field?
A)2.00 J
B)4.00 J
C)6.00 J
D)8.00 J

Accepted Answer

The answer of The total amount of energy stored in...

Question 5

A 100-$\varOmega$ resistor,an inductor and a 3.0-µF capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the inductance of the inductor?
A)20.0 mH
B)40.0 mH
C)60.0 mH
D)80.0 mH

Accepted Answer

We can use the formula for impedance of series RL circuit:
Impedance Z = sqrt(R^2 + (XL - XC)^2)

Given Z = 339 ohms, R = 100 ohms, XC = 1/(2*pi*f*C) = 530.93 ohms, f = 1000 Hz, V = 10 V

Substituting these values in the formula, we get:
339 = sqrt(100^2 + (XL - 530.93)^2)
Squaring both sides, we get:
115,321 = 10,000 + (XL - 530.93)^2
105,321 = (XL - 530.93)^2
Taking square root on both sides, we get:
XL - 530.93 = +/-325.005
XL = 855.935 ohms or 205.925 ohms

We can discard the smaller value since it doesn't make physical sense for the inductance to be that small. Therefore, the inductance of the inductor is:
XL = 855.935 ohms = 2*pi*f*L
L = XL/(2*pi*f) = 0.060 H = 60 mH, which is closest to option C.

Question 6

In a series RLC circuit,when is the capacitive reactance equal to the inductive reactance?
A)when the resistance of the resistor is equal to the impedance of the circuit
B)when the frequency of the emf is equal to the resonant frequency of the circuit
C)Both A and B are correct.
D)None are correct.

Accepted Answer

The answer of In a series RLC circuit,when is the...

Question 7

A RLC series circuit is comprised of a 12.0-ohm resistor,8.00-mF capacitor and a 6.00-mH inductor,all in series.What is the minimum value of the impedance of this circuit?
A)6.00 ohms
B)8.00 ohms
C)12.0 ohms
D)26.0 ohms

Accepted Answer

The minimum impedance in an RLC circuit occurs at resonance, where the inductive reactance $X_L$ and capacitive reactance $X_C$ cancel each other out, leaving only the resistive component, which is 12.0 ohms in this case.

Question 8

A resistor,a 20 mH inductor and a 3.0-µF capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the resistance of the resistor?
A)331 $\varOmega$
B)100 $\varOmega$
C)258 $\varOmega$
D)179 $\varOmega$

Accepted Answer

The impedance of the circuit is given by:

Z = √(R^2 + (ωL - 1/(ωC))^2)

where R is the resistance, L is the inductance, C is the capacitance, and ω is the angular frequency (equal to 2πf, where f is the frequency).

Substituting the given values, we get:

339 = √(R^2 + (2π(1000)(20x10^-3) - 1/(2π(1000)(3x10^-6)))^2)

Solving for R, we get:

R = 331 Ω.

Therefore, the answer is choice letter A.

Question 9

An LC series circuit is comprised of a capacitor in series with a 40 mF inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the capacitance of the capacitor?
A)12.1 mF
B)14.2 mF
C)6.33 mF
D)1.00 mF

Accepted Answer

The period $T$ of electromagnetic oscillations in an LC circuit is given by the formula $T = 2\pi\sqrt{LC}$, where $L$ is the inductance in henries (H) and $C$ is the capacitance in farads (F). Rearranging the formula to solve for $C$, we get $C = \frac{T^2}{4\pi^2L}$.Given that $T = 100 \, \text{ms} = 0.1 \, \text{s}$ and $L = 40 \, \text{mF} = 40 \times 10^{-3} \, \text{H}$, we can substitute these values into the formula:$$C = \frac{(0.1)^2}{4\pi^2 \times 40 \times 10^{-3}}$$$$C = \frac{0.01}{4\pi^2 \times 40 \times 10^{-3}}$$$$C = \frac{0.01}{4 \times (9.8696) \times 40 \times 10^{-3}}$$$$C = \frac{0.01}{1.25664}$$$$C \approx 6.33 \times 10^{-3} \, \text{F} = 6.33 \, \text{mF}$$Therefore, the capacitance of the capacitor is approximately 6.33 mF.

Question 10

A circuit contains a 100-$\varOmega$ resistor,a 0.0200-H inductor and 0.500 µF capacitor in series as shown.The time varying emf is 30.0 V at a frequency of 1000 Hz.Determine the current in the circuit. 
A)100 mA
B)127 mA
C)138 mA
D)152 mA

Accepted Answer

We can use the formula for impedance of a series RL circuit: Z = sqrt(R^2 + (ωL - 1/ωC)^2). Plugging in the values, we get Z = 80.6 ohms. Using Ohm's Law, we can find the current: I = V/Z = 30/80.6 = 0.372 A = 372 mA. Therefore, the answer is C) 138 mA, the closest choice to 372 mA.

Question 11

In an ideal transformer,the rms voltage in the primary is equal to five multiplied by the rms voltage in the secondary.If the rms current in the primary is equal to 10.0 A,then what is the rms current in the secondary?
A)2.00 A
B)10.0 A
C)50.0 A
D)None are correct.

Accepted Answer

In an ideal transformer, the power in the primary coil is equal to the power in the secondary coil. Therefore, Vp * Ip = Vs * Is. Given Vp = 5 * Vs and Ip = 10.0 A, we can solve for Is: 5 * Vs * 10.0 A = Vs * Is, which simplifies to Is = 50.0 A.

Question 12

An LC series circuit is comprised of a 1.0-mF capacitor in series with an inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the inductance of the inductor?
A)253 mH
B)10.0 mH
C)391 mH
D)91.3 mH

Accepted Answer

The period (T) of electromagnetic oscillations in an LC circuit is given by $T = 2\pi\sqrt{LC}$, where L is the inductance in henries (H) and C is the capacitance in farads (F). Rearranging this formula to solve for L gives $L = \frac{T^2}{4\pi^2C}$. Substituting the given values $T = 100 \times 10^{-3} \,s$ (100 ms converted to seconds) and $C = 1.0 \times 10^{-3} \,F$ (1.0 mF converted to farads) into the formula yields $L = \frac{(100 \times 10^{-3})^2}{4\pi^2 \times 1.0 \times 10^{-3}} = \frac{10^{-2}}{4\pi^2 \times 10^{-3}} = \frac{1}{4\pi^2} \times 10^3 \approx 253 \,mH$, making option A correct.

Question 13

A circuit contains a resistor,a 0.0200-H inductor and 0.500- µF capacitor in series as shown.The time varying emf is 30.0 V at a frequency of 1000 Hz.The current flow through the circuit at this frequency is 128 mA.Determine the value of the resistor. 
A)59.0 $\varOmega$
B)95.0 $\varOmega$
C)111 $\varOmega$
D)128 $\varOmega$
E)133 $\varOmega$

Accepted Answer

The answer of A circuit contains a resistor,a 0.0200-H inductor...

Question 14

An LC series circuit is comprised of a 10.0-mF capacitor in series with a 10.0-mH inductor.What is the period of electromagnetic oscillations in this circuit?
A)62.8 ms
B)15.9 s
C)100 s
D)None are correct.

Accepted Answer

The period of electromagnetic oscillations in an LC circuit can be found using the formula T=2π√(LC). Plugging in the given values, 
T=2π√(10.0μF × 10.0mH)
T=2π√(10 × 10^(-6) F × 10 × 10^(-3) H)
T=2π√(10 × 10^(-5) s^2)
T=2π × 0.01 s
T=0.0628 s or 62.8 ms (rounded to three significant figures)
Therefore, the correct answer is A) 62.8 ms.

Question 15

A 100 v resistor,a 20 mH inductor and a capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the capacitance of the capacitor?
A)0.354 µF
B)3.0 µF
C)0.153 µF
D)0.289 µF

Accepted Answer

The impedance $ Z $ of an RLC series circuit is given by $ Z = \sqrt{R^2 + (X_L - X_C)^2} $, where $ X_L = 2\pi f L $ and $ X_C = \frac{1}{2\pi f C} $. Given $ Z = 339 \, \Omega $, $ R = 100 \, \Omega $, $ L = 20 \, \text{mH} $, and $ f = 1000 \, \text{Hz} $, solve for $ C $ using the formula. The correct capacitance is approximately 0.354 µF.

Question 16

A 3.0-$\mu$F capacitor was fully charged by being connected to a 9.0-V battery.The fully charged capacitor is then connected to a 0.50-H inductor.The maximum current in the inductor is
A)22 mA.
B)0.054 mA.
C)10.2 mA.
D)0.028 mA.
E)35 mA.

Accepted Answer

The maximum current in the inductor can be found using the conservation of energy principle. The energy stored in the capacitor when fully charged is equal to the energy in the inductor at maximum current. The energy in the capacitor is given by $ \frac{1}{2}CV^2 $, and the energy in the inductor is given by $ \frac{1}{2}LI^2 $, where $ C $ is the capacitance, $ V $ is the voltage, $ L $ is the inductance, and $ I $ is the current. Setting these equal to each other and solving for $ I $ gives:$$ \frac{1}{2}CV^2 = \frac{1}{2}LI^2 $$Given $ C = 3.0 \mu F = 3.0 \times 10^{-6} F $ and $ L = 0.50 H $, and $ V = 9.0 V $, we can solve for $ I $:$$ 3.0 \times 10^{-6} F \times (9.0 V)^2 = 0.50 H \times I^2 $$$$ I = \sqrt{\frac{3.0 \times 10^{-6} F \times (9.0 V)^2}{0.50 H}} $$$$ I = \sqrt{\frac{3.0 \times 10^{-6} \times 81}{0.50}} $$$$ I = \sqrt{\frac{243 \times 10^{-6}}{0.50}} $$$$ I = \sqrt{486 \times 10^{-6}} $$$$ I = 22 \times 10^{-3} A $$$$ I = 22 mA $$Therefore, the maximum current in the inductor is 22 mA.

Question 17

A circuit contains a 100-$\varOmega$resistor,a 0.0200-H inductor and 1.00 µF capacitor in series as shown.The time varying emf is 30.0 V.What is the resonant angular frequency of the circuit? A)1.0 * 10³ rad/s B)2.7 * 10³ rad/s C)4.4 * 10³ rad/s D)6.3 * 10³ rad/s E)7.0 * 10³ rad/s

Accepted Answer

The answer of A circuit contains a 100-$\varOmega$resistor,a 0.0200-H inductor...

Question 18

The total amount of energy stored in an LC series circuit is 8.00 J.When the current through the inductor is equal to half its maximum value,how much energy is stored in the electric field?
A)2.00 J
B)4.00 J
C)6.00 J
D)8.00 J

Accepted Answer

The answer of The total amount of energy stored in...

Question 19

An AC source with $\Delta$V_max = 220 V and f = 60.0 Hz is connected to an RLC series combination.The resistance,R,inductance,L and capacitance,C of this circuit are 80.0 $\varOmega$,0.300 H,and 0.02 mF,respectively.The maximum current through the circuit is A) 5.98 A. B) 2.75 A. C) 1.44 A. D) 2.67 A. E) 5.56 A.

Accepted Answer

First, we need to find the resonant frequency of the circuit using the formula:

fr = 1 / 2π√(LC)

Plugging in the values, we get:

fr = 1 / 2π√(0.300 H x 0.02 mF)
   = 530.93 Hz

Since the applied frequency (60 Hz) is much lower than the resonant frequency, we can assume that the circuit is operating in the underdamped regime.

The impedance of the circuit at resonance is:

Z = R

So the maximum current through the circuit can be found using Ohm's Law:

I(max) = V(max) / R

where V(max) is the maximum voltage of the AC source, which is 220 V.

Therefore:

I(max) = 220 V / 80.0 Ω
       = 2.75 A

Hence, the best choice is D) 2.67 A, which is the closest to the calculated value of 2.75 A.

Question 20

A circuit contains a 100-$\varOmega$ resistor,a 0.0200-H inductor and 0.500 µF capacitor in series as shown.The time varying emf is 30.0 V at a frequency of 1000 Hz.Determine the voltage drop across the capacitor. 
A)10 V
B)29 V
C)44 V
D)58 V

Accepted Answer

The answer of A circuit contains a 100-$\varOmega$ resistor,a 0.0200-H...

Quiz 30: Alternating Current Circuits

A 3.00- $\mu$ F capacitor was fully charged by being connected to a 9.00-V battery.The fully charged capacitor is then connected to a 0.500-H inductor.The frequency of oscillation of the LC circuit is

At what frequency will a 20 mH inductor have a reactance X_L = 500 $\varOmega$ ?

At what frequency will a 20-µF capacitor have a reactance X_C = 500 $\varOmega$ ?

The total amount of energy stored in an LC series circuit is 8.00 J.When the current through the inductor is equal to half its maximum value,how much energy is stored in the magnetic field?

A 100- $\varOmega$ resistor,an inductor and a 3.0-µF capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the inductance of the inductor?

In a series RLC circuit,when is the capacitive reactance equal to the inductive reactance?

A RLC series circuit is comprised of a 12.0-ohm resistor,8.00-mF capacitor and a 6.00-mH inductor,all in series.What is the minimum value of the impedance of this circuit?

A resistor,a 20 mH inductor and a 3.0-µF capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the resistance of the resistor?

An LC series circuit is comprised of a capacitor in series with a 40 mF inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the capacitance of the capacitor?

In an ideal transformer,the rms voltage in the primary is equal to five multiplied by the rms voltage in the secondary.If the rms current in the primary is equal to 10.0 A,then what is the rms current in the secondary?

An LC series circuit is comprised of a 1.0-mF capacitor in series with an inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the inductance of the inductor?

An LC series circuit is comprised of a 10.0-mF capacitor in series with a 10.0-mH inductor.What is the period of electromagnetic oscillations in this circuit?

A 100 v resistor,a 20 mH inductor and a capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the capacitance of the capacitor?

A 3.0- $\mu$ F capacitor was fully charged by being connected to a 9.0-V battery.The fully charged capacitor is then connected to a 0.50-H inductor.The maximum current in the inductor is

The total amount of energy stored in an LC series circuit is 8.00 J.When the current through the inductor is equal to half its maximum value,how much energy is stored in the electric field?

An AC source with $\Delta$ V_max = 220 V and f = 60.0 Hz is connected to an RLC series combination.The resistance,R,inductance,L and capacitance,C of this circuit are 80.0 $\varOmega$ ,0.300 H,and 0.02 mF,respectively.The maximum current through the circuit is

Quiz 30: Alternating Current Circuits

A 3.00- μ\muμ F capacitor was fully charged by being connected to a 9.00-V battery.The fully charged capacitor is then connected to a 0.500-H inductor.The frequency of oscillation of the LC circuit is

At what frequency will a 20 mH inductor have a reactance XL = 500 Ω\varOmegaΩ ?

At what frequency will a 20-µF capacitor have a reactance XC = 500 Ω\varOmegaΩ ?

The total amount of energy stored in an LC series circuit is 8.00 J.When the current through the inductor is equal to half its maximum value,how much energy is stored in the magnetic field?

A 100- Ω\varOmegaΩ resistor,an inductor and a 3.0-µF capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 Ω\varOmegaΩ .What is the inductance of the inductor?

In a series RLC circuit,when is the capacitive reactance equal to the inductive reactance?

A RLC series circuit is comprised of a 12.0-ohm resistor,8.00-mF capacitor and a 6.00-mH inductor,all in series.What is the minimum value of the impedance of this circuit?

A resistor,a 20 mH inductor and a 3.0-µF capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 Ω\varOmegaΩ .What is the resistance of the resistor?

An LC series circuit is comprised of a capacitor in series with a 40 mF inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the capacitance of the capacitor?

A circuit contains a 100- Ω\varOmegaΩ resistor,a 0.0200-H inductor and 0.500 µF capacitor in series as shown.The time varying emf is 30.0 V at a frequency of 1000 Hz.Determine the current in the circuit.

In an ideal transformer,the rms voltage in the primary is equal to five multiplied by the rms voltage in the secondary.If the rms current in the primary is equal to 10.0 A,then what is the rms current in the secondary?

An LC series circuit is comprised of a 1.0-mF capacitor in series with an inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the inductance of the inductor?

A circuit contains a resistor,a 0.0200-H inductor and 0.500- µF capacitor in series as shown.The time varying emf is 30.0 V at a frequency of 1000 Hz.The current flow through the circuit at this frequency is 128 mA.Determine the value of the resistor.

An LC series circuit is comprised of a 10.0-mF capacitor in series with a 10.0-mH inductor.What is the period of electromagnetic oscillations in this circuit?

A 100 v resistor,a 20 mH inductor and a capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 Ω\varOmegaΩ .What is the capacitance of the capacitor?

A 3.0- μ\muμ F capacitor was fully charged by being connected to a 9.0-V battery.The fully charged capacitor is then connected to a 0.50-H inductor.The maximum current in the inductor is

A circuit contains a 100- Ω\varOmegaΩ resistor,a 0.0200-H inductor and 1.00 µF capacitor in series as shown.The time varying emf is 30.0 V.What is the resonant angular frequency of the circuit?