Consider a mutual inductor shown as below where the self-inductance L1 and L2 are known, butthe mutual inductance M is unknown. We have a standard 220V 50 Hz power supply, an ACamperemeter, and two resistors R1 and R2 (with known resistance). Construct a circuit to measure themutual inductance M. To explain your method, (i) sketch the circuit below, (ii) indicate what tomeasure, and (iii) demonstrate how to calculate the mutual inductance M and the coupling coefficientk

To measure the mutual inductance M of the given mutual inductor, we can construct a circuit as follows:

(i) Sketch the circuit:

• Connect the power supply (220V, 50Hz) to the primary coil of the mutual inductor.
• Connect an AC amperemeter in series with the primary coil.
• Connect resistors R1 and R2 in parallel to the secondary coil of the mutual inductor.
• Connect the AC amperemeter in series with resistor R1.

(ii) What to measure:

• Measure the current flowing through the AC amperemeter.

(iii) How to calculate the mutual inductance M and the coupling coefficient k:

1. Calculate the impedance of the resistors R1 and R2 in parallel using the formula: Z = R1 || R2 = (R1 * R2) / (R1 + R2).
2. Measure the current I in the circuit using the AC amperemeter.
3. Calculate the voltage across the resistors using Ohm's law: V = I * Z.
4. Calculate the voltage across the secondary coil using the formula: V2 = V * (L2 / (L1 + L2)).
5. Calculate the mutual inductance M using the formula: M = (V2 * (L1 + L2)) / (I * L1).
6. Calculate the coupling coefficient k using the formula: k = M / sqrt(L1 * L2).

By following these steps and measuring the current and voltages in the circuit, we can determine the mutual inductance M and the coupling coefficient k of the given mutual inductor.