3.1 Measure with the DMM and record the DC resistance of the 47mH inductor. Compute the value of capacitor needed to resonate with the inductor at fa . Construct a series resonant circuit consisting of the function generator, a 100Ω, 1 W resistor, one of the 47mH inductors, and a fixed lumped capacitor. Use the nearest single standard size fixed capacitor available in the laboratory for this circuit.

1. **Measure the DC Resistance**: Using the digital multimeter (DMM), measure the DC resistance of the 47 mH inductor. Record this value, which is typically small for inductors but essential to know for accurate analysis in AC circuits.

2. **Calculate Resonant Frequency \( f_a \)**: Determine the desired resonant frequency \( f_a \) for your circuit if not already specified, as this will affect the capacitor value calculation.

3. **Compute Capacitance for Resonance**: For resonance in an LC circuit, the resonant frequency \( f \) is given by:

   \[
   f = \frac{1}{2 \pi \sqrt{L C}}
   \]

   Rearranging to find the capacitance \( C \):

   \[
   C = \frac{1}{(2 \pi f)^2 L}
   \]

   Substitute \( L = 47 \, \text{mH} = 0.047 \, \text{H} \) and \( f = f_a \) into the equation to compute \( C \). 

4. **Select Nearest Standard Capacitor**: Based on your calculated capacitance, choose the nearest standard capacitor value available in the lab. Standard capacitor values are often in ranges like 10 pF, 100 pF, 1 nF, etc. 

5. **Construct the Series Resonant Circuit**: 
   - Connect the function generator in series with the 100 Ω resistor, the 47 mH inductor, and the chosen capacitor. 
   - Ensure all components are connected in series for a straightforward series resonance setup.

6. **Test and Verify Resonance**: Once assembled, use the function generator to sweep across frequencies around \( f_a \) to observe the resonance effect, where the impedance of the LC combination is minimized and the current peaks.

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Would you like a more detailed breakdown of each step?

Here are 5 follow-up questions you might find useful:

1. How do I verify that resonance is achieved in the circuit?
2. Why is it necessary to measure the DC resistance of the inductor?
3. What are typical standard capacitor values if my calculated \( C \) doesn’t match exactly?
4. How would the presence of inductor resistance affect the resonance frequency?
5. Can I replace the fixed capacitor with a variable capacitor for fine-tuning?

**Tip**: Use an oscilloscope to observe voltage across components at resonance to see the characteristic peak or dip expected in series resonant circuits.

3.1 Measure with the DMM and record the DC resistance of the 47mH inductor. Compute the value of capacitor needed to resonate with the inductor at fa. Construct a series resonant circuit consisting of the function generator, a 100Ω, 1 W resistor, one of the 47mH inductors, and a fixed lumped capacitor. Use the nearest single standard size fixed capacitor available in the laboratory for this circuit.

Learn how to measure the DC resistance of a 47mH inductor and calculate the required capacitance to resonate at a specific frequency in an LC circuit. This solution guides through constructing a series resonant circuit with a 100Ω resistor, function generator, and selecting the nearest standard capacitor for laboratory setup. Ideal for undergraduate electrical engineering students.

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