Question

A 500 Ω resistor and a 280 mH inductor are connected in series with an ac generator with an rms voltage of 23.0 V and a frequency of 65.0 Hz

What is the rms current in this circuit?

I(rms)= ? mA

Answer 1

Answer 2

Given:

• Resistor (R): 500 Ω

• Inductor (L): 280 mH = 0.280 H

• RMS Voltage (V_rms): 23.0 V

• Frequency (f): 65.0 Hz

• 
  

Step 1: Calculate the Inductive Reactance (X_L)

The inductive reactance is given by:

$$X_L=2\pi fL$$

Substitute the values:

$$X_L=2\pi \times 65.0\times 0.280=114.35\mathrm{\Omega }$$

Step 2: Calculate the Total Impedance (Z)

The impedance of the series RL circuit is:

$$Z=\sqrt{R^2+X_L^2}$$

Substitute the values:

$$Z=\sqrt{500^2+114.35^2}=\sqrt{250000+13076}=\sqrt{263076}=512.91\mathrm{\Omega }$$

Step 3: Calculate the RMS Current (I_rms)

The rms current is given by:

$$I_{\text{rms}}=\frac{V_{\text{rms}}}{Z}$$

Substitute the values:

$$I_{\text{rms}}=\frac{23.0}{512.91}=0.0448\text{A}=44.8\text{mA}$$

Final Answer:

$$\boxed{{\displaystyle 44.8\text{mA}}}$$