Calculating Currents & Voltages of an RLC Circuit

In summary, an RLC circuit with a 15Ω resistor, a 200μF capacitor, and a 12mH inductor in series has a current of 1.75A⋅cos(250πt) through each component. The voltage across the power source is V=26.79V⋅cos(250πt+0.201), the resistor is V=26.25V⋅cos(250πt), the capacitor is V=11.14⋅cos(250πt-(π/2)), and the inductor is V=16.49⋅cos(250πt+(π/2)). These values were found using the equations
  • #1
Chemmjr18
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1

Homework Statement


An RLC circuit contains the following components in series: a 15Ω resistor, a 200μF capacitor, and a 12mH inductor. What are the currents and voltages through each component?

It's known that the current through the resistor is 1.75A⋅cos(250πt)

Homework Equations


χL=ω*L
χC=1/(ωC)
Z=√(R2+(χLC)2)
φ=tan-1((χLC)/R)
Vi=Ii*Z

The Attempt at a Solution


This what I got when solving:

The current through each component is the same. I=1.75A⋅cos(250πt)

The voltage across the power source is V=26.79V⋅cos(250πt+0.201)

The voltage across the resistor is V=26.25V⋅cos(250πt)

The voltage across the capacitor is V=11.14⋅cos(250πt-(π/2))

The voltage across the inductor is V=16.49⋅cos(250πt+(π/2))
 
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  • #2
I got the same thing.
 
Last edited:
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  • #3
scottdave said:
I gotthe same thing.
Victory! Thanks!
 
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Related to Calculating Currents & Voltages of an RLC Circuit

1. How do you calculate the total current in an RLC circuit?

To calculate the total current in an RLC circuit, you can use Ohm's Law (I=V/R) where I is the current, V is the voltage, and R is the total resistance. Alternatively, you can use Kirchhoff's Laws to analyze the circuit and determine the total current.

2. What is the difference between AC and DC circuits?

In an AC (alternating current) circuit, the current is constantly changing direction, while in a DC (direct current) circuit, the current flows in one direction only. AC circuits typically use a sinusoidal waveform, while DC circuits use a constant voltage.

3. How do you calculate the voltage across a capacitor in an RLC circuit?

The voltage across a capacitor in an RLC circuit can be calculated using the formula V=Q/C, where V is the voltage, Q is the charge on the capacitor, and C is the capacitance of the capacitor. It can also be calculated using Kirchhoff's Laws.

4. What is resonance in an RLC circuit?

Resonance in an RLC circuit occurs when the circuit's reactance (XL-XC) is equal to 0, resulting in a maximum current and minimum impedance. This leads to the circuit oscillating at its natural frequency, which can be found using the formula f=1/2π√(LC), where f is the frequency, L is the inductance, and C is the capacitance.

5. How do you analyze a series RLC circuit?

To analyze a series RLC circuit, you can use Kirchhoff's Laws to create a system of equations that can be solved to find the current, voltage, and other parameters in the circuit. Alternatively, you can use phasor analysis, which involves converting the circuit's components into their corresponding phasor representations and using complex arithmetic to solve for the circuit's parameters.

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