(6) Find a formula for the inductance based on the formula above. In the a circuit like the one in the above diagram with a resistance of 100 Ω is measured with an oscilloscope. The voltage amplitude on channel 1 was 1.51 V and on channel 2 was 270 mV. (7) Calculate the current amplitude based on the fact that channel 2 measures the voltage across just the 100 Ω resistor. The frequency measured was 20.05 kHz. (8) Calculate the angular frequency of the AC source. The angular frequency should appear in the formula you found in (6), along with other quantities like the voltage amplitude of the power source, which was 1.51 V measured on channel 1. (9) Based on the formula you found, the quantities you calculated, and the known resistance, calculate the inductance in the circuit. Is it reasonably close to the 3.5 mH inductance measured for the solenoid in a previous lab? Note that at high frequencies there are a couple effects that might've added resistance to the solenoid, so agreement might not be expected to be as good as it was for the capacitor. (10) When the frequency is large, what happens to the AC current in an inductor? When the frequency is small, what happens to the AC current in an inductor? What's the upper limit on current when an inductor is in series with a resistor in AC and at what kinds of frequencies does it occur?
(6) Find a formula for the inductance based on the formula above. In the a circuit like the one in the above diagram with a resistance of 100 Ω is measured with an oscilloscope.
The voltage amplitude on channel 1 was 1.51 V and on channel 2 was 270 mV. (7) Calculate the current amplitude based on the fact that channel 2 measures the voltage across just the 100 Ω resistor. The frequency measured was 20.05 kHz.
(8) Calculate the angular frequency of the AC source. The angular frequency should appear in the formula you found in (6), along with other quantities like the voltage amplitude of the power source, which was 1.51 V measured on channel 1.
(9) Based on the formula you found, the quantities you calculated, and the known resistance, calculate the inductance in the circuit. Is it reasonably close to the 3.5 mH inductance measured for the solenoid in a previous lab?
Note that at high frequencies there are a couple effects that might've added resistance to the solenoid, so agreement might not be expected to be as good as it was for the capacitor.
(10) When the frequency is large, what happens to the AC current in an inductor? When the frequency is small, what happens to the AC current in an inductor? What's the upper limit on current when an inductor is in series with a resistor in AC and at what kinds of frequencies does it occur?
![**Inductors in AC**
The following diagram shows a circuit with an AC power source, an inductor, and a resistor, with connections to the channels of an oscilloscope indicated.
**Diagram Description:**
- The circuit contains an AC voltage source, labeled with a sine wave symbol.
- The circuit is in series with an inductor (\(L\)) and a resistor (\(R\)).
- There are connections to Channel 1 and Channel 2 of an oscilloscope, indicating measurements at different points in the circuit.
**Mathematical Explanation:**
Given an AC current \(I(t) = I \cos(\omega t)\) and source voltage \(V(t) = V \cos(\omega t + \phi)\), and that \(V(t) = V_L(t) + V_R(t)\), the following relationship is found for the circuit above:
\[V \cos(\omega t + \phi) = -I \omega L \sin(\omega t) + IR \cos(\omega t)\]
It can be shown that the following relationship holds for the amplitudes of each term in the above equation:
\[V^2 = (\omega LI)^2 + (IR)^2\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe654fef9-2f78-4c9f-8b0d-4dbb225fdff4%2Faf7a8cfa-0090-405b-8b36-ae679819080c%2Fxeeaaps_processed.jpeg&w=3840&q=75)
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