RL circuit inductive reactance problem

In summary, the problem involves a coil with resistance R=7Ω and inductance L=1mH, powered by a generator with variable frequency and Vmax=10V. The goal is to find the frequency at which the inductive reactance equals the resistance, using the equations z=R√2 and z=√(R2+(ωL)2). After plugging in z=R√2 to the second equation and solving for ω, the solution simplifies to ω=R/L, giving a frequency of 7000 Hz. However, the correct answer is 1110 Hz, which can be found by using the equation ω=2∏f.
  • #1
skate_nerd
176
0

Homework Statement



There's a coil, resistance R=7Ω, and inductance L=1mH, and its powered by a generator with variable frequency and Vmax=10V.
At what frequency is inductive reactance equal to resistance? (when z=R√2)

Homework Equations



z=R√2, z=√(R2+(ωL)2)

The Attempt at a Solution



I plugged in z=R√2 to z=√(R2+(ωL)2), and solved for ω. This ends up just simplifying to ω=R/L, which is 7Ω/0.001H, giving 7000Hz. But my teachers answer is 1110Hz. Am I doing something wrong here? Been stuck on this for a while.
 
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  • #2
ω has units of radians/second.
 
  • #3
Okay...isn't that basically the same thing? Frequency in measured in hertz, which is an inverse second. And also my teachers answer specifically says 1110 Hz
 
  • #4
What is the equation relating Hz to radians/sec?
 
  • #5
ahh. ω=2∏f. my bad...i don't know why i didnt recognize that. thanks!
 

FAQ: RL circuit inductive reactance problem

1. What is an RL circuit inductive reactance?

An RL circuit inductive reactance is a type of electrical resistance that occurs in a circuit containing both inductance (L) and resistance (R) components. It is caused by the magnetic field generated by the inductor, which opposes changes in current flow.

2. How is inductive reactance calculated in an RL circuit?

Inductive reactance in an RL circuit can be calculated using the formula XL = 2πfL, where XL is the inductive reactance in ohms, f is the frequency of the current in hertz, and L is the inductance in henrys.

3. What is the effect of increasing inductance on inductive reactance?

Increasing inductance in an RL circuit will increase the inductive reactance. This means that the circuit will have more resistance to changes in current flow and the voltage across the inductor will also increase.

4. How does the phase relationship between current and voltage change in an RL circuit with inductive reactance?

In an RL circuit with inductive reactance, the current and voltage have a phase difference of 90 degrees. This means that the current lags behind the voltage in the circuit.

5. How can inductive reactance be reduced in an RL circuit?

Inductive reactance can be reduced in an RL circuit by increasing the frequency of the current, decreasing the inductance, or adding a resistor in series with the inductor. This will decrease the magnetic field and its opposing effect on current flow, resulting in a lower inductive reactance.

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