Question

A series RLC circuit consists of a 50Ω resistor, a 3.3 mH inductor, and a 480 nF capacitor. It is connected to a 5.0 kHz oscillator with a peak voltage of 5.0 V.A. What is the instantaneous current i when E = E 0 ?B. What is the instantaneous current i when E =0V and is decreasing?

Answer 1

To find the instantaneous current in an RLC circuit, calculate the impedance using the resistance, inductive reactance, and capacitive reactance. Then, use Ohm's Law to calculate the current using the voltage.

Step-by-step explanation:

In order to find the instantaneous current in an RLC circuit, we need to calculate the impedance and use Ohm's Law. The impedance of an RLC circuit is given by the formula:

Z = √(R2 + (XL - XC)2)

Where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. The inductive reactance is given by XL = 2πfL, and the capacitive reactance is given by XC = 1/(2πfC).

Once we have the impedance, we can calculate the instantaneous current using the formula:

I = E / Z

where E is the voltage across the circuit.

Answer 2

To find the instantaneous current when the voltage equals its peak value E=E0 in an RLC circuit, divide the peak voltage by the resistance. When the voltage is 0V and decreasing, the current analysis involves differential calculus and impedance considerations.

Step-by-step explanation:

The question pertains to a series RLC circuit and asks about the instantaneous current at different voltage conditions. To find the instantaneous current when the voltage equals its maximum value (E = E0), we consider that this is the point where the capacitor and inductor voltages cancel each other and only the resistor affects the current, meaning I = E0/R. However, when the voltage is 0V and decreasing, understanding the oscillator behavior in a RLC circuit would entail calculating the derivative of voltage over time, which requires differential calculus and knowledge of the circuit's total impedance and phase shifts.