A 120-V rms voltage at 2000 Hz is applied to a 6.0-mH inductor, a 2.0-ìF capacitor and a 200-Ù resistor. What is the rms value of the current in this circuit?

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Xl = 2pi*F*L = 6.28*2000*0.006 = 75.4 Ohms.

Xc = 1/(2pi*F*C)=1/(6.28*2000*2*10^-6) =
39.8 Ohms.

Z = R + (Xl-Xc) = 200 + j(75.4-39.8) =
200 + j35.6 = 203 Ohms[10.1o]

I=E/Z = 120[0o]/203[10.1o]=0.59[-10.1o]
Amps.

To find the rms value of the current in the circuit, we can use Ohm's law and solve for the current (I).

First, we need to calculate the impedance (Z) of the circuit using the given values:

1. For the inductor (L):
- The inductive reactance (XL) is given by the formula: XL = 2πfL.
- Substituting the values, we get: XL = 2π(2000 Hz)(6.0 mH).

2. For the capacitor (C):
- The capacitive reactance (XC) is given by the formula: XC = 1/(2πfC).
- Substituting the values, we get: XC = 1/(2π(2000 Hz)(2.0 μF)).

3. For the resistor (R):
- The resistance (R) is given as 200 Ω.

Now, we can calculate the impedance (Z) of the circuit using the formula:

Z = √(R^2 + (XL - XC)^2).

Substituting the values, we get:

Z = √((200 Ω)^2 + (2π(2000 Hz)(6.0 mH) - 1/(2π(2000 Hz)(2.0 μF)))^2).

Once we have the value of Z, we can use Ohm's law to calculate the current (I) using the formula:

I = V / Z,

where V represents the voltage applied to the circuit.

Substituting the given voltage (V = 120 V) and calculated impedance (Z), we can solve for the current (I), which represents the rms value of the current in the circuit.

To find the rms value of the current in this circuit, we can use the concepts of impedance and Ohm's law in the context of AC circuits.

1. Calculate the impedance of the inductor (XL):
The impedance of an inductor in an AC circuit is given by the formula XL = 2πfL, where f is the frequency in Hz and L is the inductance in Henrys.
Given:
Frequency (f) = 2000 Hz
Inductance (L) = 6.0 mH = 6.0 * 10^(-3) H
XL = 2π * 2000 * (6.0 * 10^(-3))
Calculate XL using the given values.

2. Calculate the impedance of the capacitor (XC):
The impedance of a capacitor in an AC circuit is given by the formula XC = 1 / (2πfC), where f is the frequency in Hz and C is the capacitance in Farads.
Given:
Frequency (f) = 2000 Hz
Capacitance (C) = 2.0 µF = 2.0 * 10^(-6) F
XC = 1 / (2π * 2000 * (2.0 * 10^(-6)))
Calculate XC using the given values.

3. Calculate the total impedance (Z):
In this circuit, the resistor, inductor, and capacitor are in series. The total impedance (Z) is given by the formula Z = sqrt(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
Given:
Resistance (R) = 200 Ω
Calculate Z using the values of R, XL, and XC.

4. Apply Ohm's law to find the rms value of the current:
Ohm's law states that the current (I) in an AC circuit is given by the formula I = V / Z, where V is the voltage and Z is the impedance.
Given:
Voltage (V) = 120 V
Calculate the current (I) using the values of V and Z.

By following these steps and calculating the values at each step, you will be able to find the rms value of the current in this circuit.