Problem 3: A circuit has 1000 turns enclosing a magnetic circuit 20 cm^{2} in section. With 4 A current, the flux density is 1 Wbm^{-2} and with 9 A current, it is 1.4 Wbm^{-2}. Find the mean value of the inductance between these limits and the induced emf, if the current falls 9 A to 4 A in 0.05 seconds.

Solution

Given data No of turns in the circuit = 1000

Area enclosed =

Case 1: Current flowing in the circuit, I_{1} = 4 Amp, Flux density, Ф_{1} = 1 Wb m^{-2}

Case 2: Current flowing in the circuit, I_{2} = 9 Amp, Flux density, Ф_{2} = 1.4 Wbm^{-2}

Time for the change in current = 0.05 sec

Required Mean value of inductance, L =? Induced emf, ε =?

Formulae

Now from the given data, ΔB = 1.4 – 1.0 = 0.4 Wb m^{-2}

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