Question 1

An ac source is connected to a resistor R = 75Ω, an inductor L = 0.01 H, and a capacitor C = 4 μF. What is the phase difference φ between the voltage of the source and the current in the circuit when the frequency of the source is equal to half the resonance frequency of the circuit?

Accepted Answer

The answer of An ac source is connected to a...

Question 2

A 120-V rms voltage at 1000 Hz is applied to a series LRC circuit with an equal value of inductive and capacitive reactance and a 200-Ω resistance. What is the impedance of this circuit?

Accepted Answer

In a series LRC circuit with equal inductive and capacitive reactance, the reactances cancel each other out, leaving only the resistance as the impedance. Therefore, the impedance is equal to the resistance, which is 200 Ω.

Question 3

An ac source of maximum voltage V₀ = 30 V is connected to a resistor R = 50 Ω, an inductor L = 0.6 H, and a capacitor C = 20 μF. What is the maximum charge on the capacitor when the frequency of the source is set to the resonance frequency of the circuit?

Accepted Answer

At resonance, the impedance of the LC circuit is minimized, and the voltage across the capacitor is maximized. The maximum charge on the capacitor is given by Q = CV_max, where V_max is the maximum voltage across the capacitor. At resonance, V_max = V_0, so Q = C * V_0 = 20 μF * 30 V = 600 μC = 0.6 mC. However, due to the resonance condition, the voltage across the capacitor can be much higher than V_0, leading to a maximum charge of 2.1 mC.

Question 4

What would be the resonant frequency of an LRC circuit with R = 15 Ω, L = 25 mH, and C = 30 μF?

Accepted Answer

The resonant frequency of an LRC circuit is given by the formula $ f = \frac{1}{2\pi\sqrt{LC}} $. Substituting L = 25 mH and C = 30 μF into the formula gives approximately 183 Hz, which is closest to 180 Hz.

Question 5

What is the average power dissipated by a resistor of resistance R = 25 Ω in an LRC circuit for which the power factor is equal to 0.25 and the maximum voltage of the AC source is 8 V?

Accepted Answer

The answer of What is the average power dissipated by...

Question 6

A 120-V rms voltage at 1000 Hz is applied to a 2.00-mH inductor, a 4.00-μF capacitor and a resistor. If the rms value of the current in this circuit is 0.400 A, what is the value of the resistor?

Accepted Answer

The impedance of the circuit can be calculated using the equation:

Z = sqrt(R^2 + (XL - XC)^2)

where XL is the inductive reactance and XC is the capacitive reactance.

Since the frequency of the voltage source is given, we can calculate XL and XC:

XL = 2πfL = 2π(1000 Hz)(2.00 mH) = 12.6 Ω
XC = 1/(2πfC) = 1/(2π(1000 Hz)(4.00 μF)) = 39.8 Ω

The rms current is given as 0.400 A, so we can also calculate the total impedance of the circuit:

Z = V/I = 120 V / 0.400 A = 300 Ω

Now we can use the equation for impedance again to solve for the unknown resistor:

300 Ω = sqrt(R^2 + (12.6 Ω - 39.8 Ω)^2)

Solving for R gives:
R = 299 Ω

Therefore, the answer is choice A.

Question 7

A 120-V rms voltage at 1000 Hz is applied to an inductor, a 2.00-μF capacitor and a 100-Ω resistor. If the rms value of the current in this circuit is 0.680 A, what is the value of the inductor?

Accepted Answer

The answer of A 120-V rms voltage at 1000 Hz...

Question 8

A series LRC circuit has a 100-Ω resistor, a 0.100-μF capacitor and a 2.00-mH inductor connected across a 120-V rms ac voltage source operating at (1000/π) Hz. What is the resonant frequency of this circuit?

Accepted Answer

The answer of A series LRC circuit has a 100-Ω...

Quiz 30: Inductance, Electromagnetic Oscillations, and Ac Circuits