# RCL circuit alternating current, calculate current sum

• Engineering
• znaya
In summary, the current ix(t) in the given circuit is 9.9 cos(2t - 129.2º) as calculated using superposition method.
znaya

## Homework Statement

Consider, in the circuit from the image,
i1(t) = 5 cos(2t + 10º)
v1(t) = 10 cos(2t - 60º).

Find the value of the current ix(t).

Options given:

A: ix(t) = 9.9 cos(2t - 129.2º)
B: ix(t) = 9 cos(2t - 29.2º)
C: ix(t) = 99 cos(2t + 129.2º)
D: ix(t) = 0.99 cos(2t + 130º)

Ohm's law.
V=IR

## The Attempt at a Solution

My approach was, first calculate the amount of current produced by the voltage source, combining the R + C + L in series and ignoring the current source, the result was 2<-59º(or 1.03 -1.7j)
After I calculated the amount of current from the current source. I ignored the voltage source (short circuiting the circuit) and calculated L || (C + R) and the amount of current going to (C + R) is 11.86<-25.3º (or 10.7 -5.06j).

Finally i summed the currents:

1.03-1.7j + -(10.7-5.06j) ====> negative because it goes in the opposite direction from the one in the image.
The result was -9.67+3.36j or 99.7<-19.16º [+180º];
That is 99.7 < 160.84º or 99.7 cos(2t + 160.84º)
That is near option C but not exactly! What am I doing wrong?

Thanks for any help.

Can you show your calculations of the superposition currents in more detail? The values you're getting don't look right according to my own working, so I'd like to see how you're carrying out the operations.

Hi.

I reviewed all my calculations, I had huge mistakes all over!

The current produced by the voltage source should be 2<-113º (or -0.78-1.84j).
The amount of current from the current source (using a current divider) should be 8<47º (or 5.46+5.85j).

-0.78-1.84j - (5.46+5.85j) = -6.24-7.69j

-6.24-7.69j = 9.90<50.94º

ix(t) = 9.9cos(2t + 50.94º) = 9.9cos(2t - 129.06º) [because cos(50.94º) = cos(-129.06º)]

So... option A is correct.

## 1. What is an RCL circuit?

An RCL circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) connected in series or in parallel. It is used to control the flow of current and voltage in an alternating current (AC) circuit.

## 2. How does an RCL circuit work?

The resistor, inductor, and capacitor in an RCL circuit work together to create a circuit that can store and release energy. The resistor controls the amount of current flowing through the circuit, the inductor stores energy in a magnetic field, and the capacitor stores energy in an electric field. The combination of these components creates a circuit that can oscillate or resonate at a specific frequency.

## 3. What is alternating current (AC)?

Alternating current is an electric current that reverses direction at regular intervals. This is in contrast to direct current (DC) which flows in only one direction. AC is the type of current that is supplied by power plants and used in most household and industrial electrical systems.

## 4. How do you calculate the current sum in an RCL circuit?

The current sum in an RCL circuit can be calculated using Ohm's Law and Kirchhoff's Laws. First, determine the total impedance of the circuit by adding the resistive, inductive, and capacitive components. Then, use Ohm's Law (V = IR) to calculate the total current. Finally, use Kirchhoff's Laws to calculate the individual currents in each component. The sum of these currents will equal the total current in the circuit.

## 5. What are some practical applications of RCL circuits?

RCL circuits have many practical applications, including in radio receivers, filters, and oscillators. They are also used in power factor correction, which helps improve the efficiency of electrical systems. RCL circuits are also used in electronic devices such as computers, TVs, and smartphones to control the flow of current and voltage and prevent damage to the device.

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