Question 1

An RLC series circuit has a 400 Ω resistance, a 2.50 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms current at resonance?

Accepted Answer

The resonant frequency can be calculated using the formula: 
f = 1/2π√(LC)

Where L is the inductance and C is the capacitance.

Given: 
R = 400 Ω
L = 2.50 mH = 0.00250 H
f = 30.0 kHz

We can rearrange the formula to solve for capacitance:

C = 1/((2πf)^2L)

C = 1/((2π × 30.0 kHz)^2 × 0.00250 H) ≈ 51.9 nF

The impedance of the circuit can be calculated as:

Z = √(R^2 + (ωL - 1/ωC)^2)

At resonance, ωL = 1/ωC, so the equation becomes:

Z = R

Therefore, the rms current at resonance can be calculated as:

I = V/R = 20 mV / 400 Ω = 50 μA

So, the correct choice is D.

Question 2

In a series RLC circuit the rms voltage across the resistor is 80.0 V, across the capacitor is 120 V, and across the inductor is 60.0 V. If 1.50 A rms current is flowing in this circuit, what is the average power dissipated?

Accepted Answer

The answer of In a series RLC circuit the rms...

Question 3

In a series RLC circuit the rms voltage across the resistor is 80 V, across the capacitor is 120 V, and across the inductor is 60 V. What is the phase constant for this circuit?

Accepted Answer

The answer of In a series RLC circuit the rms...

Question 4

The inductive reactance of an RLC circuit is 36 Ω. If the frequency is doubled, what is the new inductive reactance?

Accepted Answer

Inductive reactance (XL) is directly proportional to the frequency (f), given by the formula XL = 2πfL. Doubling the frequency doubles the inductive reactance, making it 72 Ω.

Question 5

A series RLC circuit has resistance 200 Ω, inductance 0.200 H, and capacitance 0.500 μF. If the circuit is at resonance with a 120 V rms source, what is the average power dissipated?

Accepted Answer

The answer of A series RLC circuit has resistance 200...

Question 6

As the ac frequency in an RLC circuit is increased to very high values, which of the contributions to the impedance dominates?

Accepted Answer

At very high frequencies, the inductive reactance dominates over the capacitive reactance, making it the main contributor to the impedance. This is because the inductive reactance increases with frequency, while the capacitive reactance decreases.

Question 7

What inductance is needed in series with a 4.7 μF capacitor for a resonant frequency of 10 kHz?

Accepted Answer

The resonant frequency of a series RLC circuit is given by:

f = 1/(2π√(LC))

Solving for L:

L = 1/(4π^2f^2C)

Substituting given values:

L = 1/(4π^2 * 10kHz^2 * 4.7μF) = 54μH

Therefore, choice B is the correct answer.

Question 8

A series RLC circuit has a resistance of 500 Ω, an inductance of 20.0 mH, and a capacitance of 2.00 μF. The source provides a voltage of v(t) = (170 V) sin (377t). What is the peak current in this circuit?

Accepted Answer

The answer of A series RLC circuit has a resistance...

Question 9

A series RLC circuit has a capacitive reactance of 16 Ω and an inductive reactance of 4.0 Ω at 30 Hz. What frequency would result in resonance for this circuit?

Accepted Answer

Resonance occurs when the capacitive reactance and inductive reactance are equal in magnitude and opposite in sign. This happens when:

1/(2*pi*f*C) = 2*pi*f*L

Simplifying this equation, we get:

f^2 = 1/(2*pi*C*L)

Plugging in the given values, we get:

f^2 = 1/(2*pi*16*4)

f^2 = 0.003125

f = 0.056 Hz

So the frequency of resonance is approximately 56 Hz. However, this is not one of the given answer choices. The closest answer choice is B, 60 Hz.

Question 10

An RLC series circuit has a 200 Ωresistance, a 3.0 mH inductor, and a 100 μF capacitor. What is the resonant frequency for this circuit?

Accepted Answer

The resonant frequency can be calculated using the formula f = 1 / (2π√(LC)). Plugging in the given values, we get f = 1 / (2π√(3.0 x 10^-3 x 100 x 10^-6)) = 290 Hz. Therefore, the best choice is C.

Question 11

What is the resonant frequency of a 1.0 μF capacitor and a 15 mH inductor in series?

Accepted Answer

The resonant frequency $f$ of a series LC circuit is given by the formula $f = \frac{1}{2\pi\sqrt{LC}}$, where $L$ is the inductance in henries (H) and $C$ is the capacitance in farads (F). Plugging in the values $L = 15 \times 10^{-3}$ H and $C = 1.0 \times 10^{-6}$ F, we get $f = \frac{1}{2\pi\sqrt{15 \times 10^{-3} \times 1.0 \times 10^{-6}}}$ which calculates to approximately 1.3 kHz.

Question 12

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the average power dissipated by the circuit at resonance?

Accepted Answer

The answer of An RLC series circuit has a 400...

Question 13

An RLC series circuit has a 22 Ω resistor, a 3.0 H inductor, and a capacitor. What capacitance would result in resonance at 60 Hz?

Accepted Answer

The answer of An RLC series circuit has a 22...

Question 14

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30 kHz, what is the capacitive reactance at resonance?

Accepted Answer

The answer of An RLC series circuit has a 400...

Question 15

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms voltage across the inductor at resonance?

Accepted Answer

The answer of An RLC series circuit has a 400...

Question 16

A series RLC circuit has a resistance of 500 Ω, an inductance of 20.0 mH, and a capacitance of 2.00 μF. The source provides a voltage of v(t) = (170 V) sin (377t). What is the impedance of this circuit?

Accepted Answer

The impedance of a series RLC circuit is given by 
$Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$, where $\omega$ is the angular frequency of the source voltage.
Substituting the given values, we get:
$Z = \sqrt{(500)^2 + (377 	imes 0.020 - \frac{1}{377 	imes 2 	imes 10^{-6}})^2}$
$Z = 1.41$ k$\Omega$ (rounded to two decimal places)
Therefore, the best choice is (D) 1.41 k$\Omega$.

Question 17

An ideal diode in an ac circuit

Accepted Answer

An ideal diode only permits current to flow in one direction, blocking it in the other direction. It does not alter the current or double/halve it.

Question 18

An RLC series circuit has a 200 Ω resistance, a 3.0 mH inductor, and a 100 μF capacitor. At resonance, what is the inductive reactance?

Accepted Answer

The answer of An RLC series circuit has a 200...

Question 19

If the inductance and the capacitance both double in an LRC series circuit, the resonant frequency of that circuit will

Accepted Answer

The resonant frequency of an LRC series circuit is given by f=1/(2π√LC). If both L and C double, the frequency will decrease because the denominator will increase by a factor of 2√2, resulting in a decrease by a factor of 1/2.

Question 20

In a series RLC circuit the rms voltage across the resistor is 80.0 V, across the capacitor is 120 V, and across the inductor is 60.0 V. What is the rms voltage applied to this circuit?

Accepted Answer

The rms voltage applied to a series RLC circuit is found by subtracting the voltage across the capacitor from the sum of the voltages across the resistor and inductor, due to the phase difference between them, and then taking the square root of the sum of the squares of these voltages. Thus, $V_{rms} = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{80^2 + (60 - 120)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 V.$

Quiz 21: Alternating Current

An RLC series circuit has a 400 Ω resistance, a 2.50 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms current at resonance?

In a series RLC circuit the rms voltage across the resistor is 80.0 V, across the capacitor is 120 V, and across the inductor is 60.0 V. If 1.50 A rms current is flowing in this circuit, what is the average power dissipated?

In a series RLC circuit the rms voltage across the resistor is 80 V, across the capacitor is 120 V, and across the inductor is 60 V. What is the phase constant for this circuit?

The inductive reactance of an RLC circuit is 36 Ω. If the frequency is doubled, what is the new inductive reactance?

A series RLC circuit has resistance 200 Ω, inductance 0.200 H, and capacitance 0.500 μF. If the circuit is at resonance with a 120 V rms source, what is the average power dissipated?

As the ac frequency in an RLC circuit is increased to very high values, which of the contributions to the impedance dominates?

What inductance is needed in series with a 4.7 μF capacitor for a resonant frequency of 10 kHz?

A series RLC circuit has a resistance of 500 Ω, an inductance of 20.0 mH, and a capacitance of 2.00 μF. The source provides a voltage of v(t) = (170 V) sin (377t) . What is the peak current in this circuit?

A series RLC circuit has a capacitive reactance of 16 Ω and an inductive reactance of 4.0 Ω at 30 Hz. What frequency would result in resonance for this circuit?

An RLC series circuit has a 200 Ωresistance, a 3.0 mH inductor, and a 100 μF capacitor. What is the resonant frequency for this circuit?

What is the resonant frequency of a 1.0 μF capacitor and a 15 mH inductor in series?

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the average power dissipated by the circuit at resonance?

An RLC series circuit has a 22 Ω resistor, a 3.0 H inductor, and a capacitor. What capacitance would result in resonance at 60 Hz?

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30 kHz, what is the capacitive reactance at resonance?

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms voltage across the inductor at resonance?

A series RLC circuit has a resistance of 500 Ω, an inductance of 20.0 mH, and a capacitance of 2.00 μF. The source provides a voltage of v(t) = (170 V) sin (377t) . What is the impedance of this circuit?

An ideal diode in an ac circuit

An RLC series circuit has a 200 Ω resistance, a 3.0 mH inductor, and a 100 μF capacitor. At resonance, what is the inductive reactance?

If the inductance and the capacitance both double in an LRC series circuit, the resonant frequency of that circuit will

In a series RLC circuit the rms voltage across the resistor is 80.0 V, across the capacitor is 120 V, and across the inductor is 60.0 V. What is the rms voltage applied to this circuit?