MATHEMATICAL INDUCTION - L2

A thin copper wire of length 100m is wound as a solenoid of length (l) and radius (1) its self inductance is found to be L. Now if same length of wire is would as a solenoid of length (I) of radius (). Then its self inductance will be A 4L B 2L C L DL/2

Prove the following by using the Principle of mathematical induction AA n in N 2^(3n-1) is divisble by 7.

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

In Fig. coil 1 and coil 2 are wound on a long cylindrical insulator. The ends A' and B are joined together and current I is passed. Self-inductance of the two coils are L_(1) and L_(2) , and their mutual inductance is M . a. Show that this combination can be replaced by a single coil of equivalent inductange given by L_(eq) = L_(1) + L_(2) + 2M . b. How could the coils be reconnected by yieldings an equivalent inductance of L_(eq) = L_(1) + L_(2) - 2M .

Prove the following by using the Principle of mathematical induction AA n in N n<2^(n)

Prove the following by using the Principle of mathematical induction AA n in N 3^(n)>2^(n)

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+3)le(n+3)!

By Principle of Mathematical Induction 1 + 2 + 3 _____ + n = _____

Mutual inductance of two coils depends on their self inductance L_(1) and L_(2) as :