What is the RMS current in milliamps (mA) in a series circuit with a resistor R = 200 2, an inductor L= 113 mH, and an AC source that provides an RMS voltage of 155 volts at 491 Hz? (State answer as an integer. Do not include unit.)
What is the RMS current in milliamps (mA) in a series circuit with a resistor R = 200 2, an inductor L= 113 mH, and an AC source that provides an RMS voltage of 155 volts at 491 Hz? (State answer as an integer. Do not include unit.)
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![**Question:**
What is the RMS current in milliamps (mA) in a series circuit with a resistor \( R = 200 \, \Omega \), an inductor \( L = 113 \, \text{mH} \), and an AC source that provides an RMS voltage of 155 volts at 491 Hz? (State answer as an integer. Do not include unit.)
**Explanation:**
This problem involves calculating the Root Mean Square (RMS) current in a series AC circuit containing both a resistor and an inductor. To find the RMS current, we need to consider both the resistance and the inductive reactance of the circuit.
1. **Calculate the Inductive Reactance (\(X_L\)):**
The inductive reactance is given by the formula:
\[
X_L = 2 \pi f L
\]
where:
- \( f = 491 \) Hz is the frequency,
- \( L = 113 \times 10^{-3} \) H is the inductance.
2. **Calculate the Impedance (\(Z\)):**
The total impedance in the circuit is:
\[
Z = \sqrt{R^2 + X_L^2}
\]
where:
- \( R = 200 \, \Omega \) is the resistance.
3. **Calculate the RMS Current (\(I_{\text{RMS}}\)):**
The RMS current is found using Ohm's Law for AC circuits:
\[
I_{\text{RMS}} = \frac{V_{\text{RMS}}}{Z}
\]
where:
- \( V_{\text{RMS}} = 155 \, \text{V} \) is the RMS voltage.
By solving these steps, you will find the RMS current value in milliamps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe729a476-2c21-47cf-8145-b09785d3a477%2F141d843a-0bef-41fd-9486-7cb5203beb50%2Fzy5vruv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the RMS current in milliamps (mA) in a series circuit with a resistor \( R = 200 \, \Omega \), an inductor \( L = 113 \, \text{mH} \), and an AC source that provides an RMS voltage of 155 volts at 491 Hz? (State answer as an integer. Do not include unit.)
**Explanation:**
This problem involves calculating the Root Mean Square (RMS) current in a series AC circuit containing both a resistor and an inductor. To find the RMS current, we need to consider both the resistance and the inductive reactance of the circuit.
1. **Calculate the Inductive Reactance (\(X_L\)):**
The inductive reactance is given by the formula:
\[
X_L = 2 \pi f L
\]
where:
- \( f = 491 \) Hz is the frequency,
- \( L = 113 \times 10^{-3} \) H is the inductance.
2. **Calculate the Impedance (\(Z\)):**
The total impedance in the circuit is:
\[
Z = \sqrt{R^2 + X_L^2}
\]
where:
- \( R = 200 \, \Omega \) is the resistance.
3. **Calculate the RMS Current (\(I_{\text{RMS}}\)):**
The RMS current is found using Ohm's Law for AC circuits:
\[
I_{\text{RMS}} = \frac{V_{\text{RMS}}}{Z}
\]
where:
- \( V_{\text{RMS}} = 155 \, \text{V} \) is the RMS voltage.
By solving these steps, you will find the RMS current value in milliamps.
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