Problem 3: A circuit has 1000 turns enclosing a magnetic circuit 20 cm2 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.
Given data No of turns in the circuit = 1000
Area enclosed =
Case 1: Current flowing in the circuit, I1 = 4 Amp, Flux density, Ф1 = 1 Wb m-2
Case 2: Current flowing in the circuit, I2 = 9 Amp, Flux density, Ф2 = 1.4 Wbm-2
Time for the change in current = 0.05 sec
Required Mean value of inductance, L =? Induced emf, ε =?
Now from the given data, ΔB = 1.4 – 1.0 = 0.4 Wb m-2
ΔI = 9 – 4 = 5 Amp
Put for the formula of inductance,
Put for the formula of emf,