A solenoid has a certain length, number of turns per meter, and a certain cross

Question

A solenoid has a certain length, number of turns per meter, and a certain cross sectional area. It has inductance of 2.0 milli-henries. If the length of the solenoid is increased by a factor of 4.7 but nothing else changes, what is the new inductance in milli-henries? A generator consists of a square coil wrapped 8 times with sides of length 0.35 m. spun at some frequency in a uniform magnetic field of 0.24 Tesla. The maximum EMF produced by the generator is 21 volts. At what frequency was the coil spun in Hz? An AC voltage source is connected to a transformer on the primary side. The maximum EMF on the secondary side is 10 volts. The number of primary turns is 171 and the number of turns on the secondary side is 42 What is the maximum primary EMF in volts?

Explanation / Answer

The inductance of a solenoid is given by

L = u N^2 A/l

As per the given condition,

L1 = 2 mH

L2 = ? ; l2 = 4.7 Ll

L1 = u N^2 A/l1

L2 = u N^2 A/(4.7 l1)

L1/L2 = u N^2 A/l1 x l2/u N^2 A = l2/l1

L1/L2 = l2/l1

L2 = L1 l1/l2 = 2 mH x l1/4.7l1 = 0.426 mH

Hence, L2 = 0.426 mH

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