Electricity and Magnetism Question (Capacitor). .

[Partap03]

Okay, I will be honest, this is a homework assignment. For that matter this is the last homework assignment which is very crucial to preparing for the final. But the problem is I have 2 more finals for which I need to study for. So if you can please help me out and give a detailed solution I will appreciate it. Thanks in advance.



A 1 micro F capacitor, a 10 ohm resistor and a 1 micro H inductor are connected in series with a sinusoidal signal generator of 10V peak voltage amplitude operating at a frequency of 100 rad/s.
a) Find the amplitude of current oscillations in the circuit.
b) Find the phase shift between the current and the generator voltage. Does the current lead the voltage or vice-versa?

 

[jbsteele]

a) The amplitude of current oscillations in the circuit can be found using Ohm's Law:I = V/R Where V is the voltage of the signal generator and R is the resistance of the 10 ohm resistor.So, I = 10/10 = 1 A.b) The phase shift between the current and the generator voltage can be calculated using the formula: phase shift = arctan(Xc/Xl)Where Xc is the capacitive reactance and Xl is the inductive reactance.Xc = 1/2πfC = 1/2π(100)(1x10^-6) = 15915.9 ohmsXl = 2πfL = 2π(100)(1x10^-6) = 6283.2 ohmsUsing the above values in the formula, the phase shift is -39.19 degrees. This means that the current lags the voltage, i.e. the current is behind the voltage by 39.19 degrees.

 

[nlightner]

I understand the importance of balancing multiple responsibilities and studying for exams. I will do my best to provide a detailed solution to your question.

First, let's start by understanding the components in the circuit. A capacitor is an electronic component that stores electrical energy in the form of an electric field. Its unit of measurement is Farad (F), and in this circuit, we are given a 1 micro F capacitor. A resistor is a component that resists the flow of current, and its unit of measurement is ohm (Ω). In this circuit, we have a 10 ohm resistor. An inductor is an electronic component that stores electrical energy in the form of a magnetic field. Its unit of measurement is Henry (H), and in this circuit, we have a 1 micro H inductor.

Now, let's solve for the amplitude of current oscillations in the circuit. We can use the formula for impedance (Z) in a series circuit, which is Z = √(R^2 + (Xl - Xc)^2), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. In this case, R = 10 Ω, Xl = ωL = (100 rad/s)(1 micro H) = 0.1 Ω, and Xc = 1/(ωC) = 1/(100 rad/s)(1 micro F) = 0.01 Ω. Therefore, Z = √(10^2 + (0.1 - 0.01)^2) = √100.09 = 10.0045 Ω.

We can now use Ohm's law (V = IZ) to solve for the current (I) in the circuit. The peak voltage amplitude is given as 10V, so V = 10V. Therefore, I = V/Z = (10V)/(10.0045 Ω) = 0.9999 A. This is the amplitude of current oscillations in the circuit.

Next, to find the phase shift between the current and the generator voltage, we need to use the formula φ = arctan((Xl - Xc)/R). In this case, φ = arctan((0.1 - 0.01)/10) = arctan(0.009) = 0.9