Will the constant of mutual inductance change? Will the value of mutual inductance be different when the initial primary coil is connected to a voltmeter and the initial secondary coil is connected to the power supply?(which means the initial primary coil is now the secondary coil) From what I thought, that constant should change as the number of primary coil and the length of the primary coil is different from initial value of the primary coil.
 A: Excellent observation! For a typical low frequency transformer the change will usually be small enough to ignore, but for an RF transformer the addition of the  wire inductances (and the additional inductive coupling they create) can alter the behavior significantly and even completely falsify the measurement. If you want to avoid problems, it is a good idea to reduce the inductances of the leads to and from the device by twisting the wires. The twisting reduces the loop area very considerably and makes it fairly constant, even when the wires move. Since the remaining magnetic flux leakage of a twisted wire constantly changes direction, it will mostly average out. While this may still not be enough to enable a precision measurement for high frequency components (that may require proper impedance matching and/or the use of a vector network analyzer that can calibrate the lead impedances out of the measurement), it will go a long way to produce stable and reproducible measurements in many applications. 
