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INDUCTANCES IN PARALLEL

In general, we have

Example 34. If a coil of 150 turns is linked with a flux of 0.01 Wb when carrying a current of 10 A; calculate the inductance of the coil. If this current is uniformly reversed in 0.1 second, calculate the induced e.m.f. If a second coil of 100 turns is uniformly wound over the first coil, find the mutual inductance between the coils.

(Pune University)

Solution. Given : N1 = 150 ɸ = 0.01 Wb ;

i1 = 10 A ;

di = 10 – (-10) = 20 A ;

dt = 0.1 s ;

N2 = 100

Induced e.m.f. L1:

Example 35. Two coils having 30 and 600 turns respectively are wound side-by-side on a closed iron circuit of cross-section 100 sq. cm. and mean length 200 cm.

(i)                           Estimate the mutual inductance between the coils if the relative permeability of the iron is 2000.

(ii)                        If a current of zero ampere grows to 20 A in a time of 0.02 second in the first coil, find the e.m.f. induced in the second coil.

(JNT University Warangal)

Solution. Given N1 = 30;

N2 = 600;

A = 100 × 10-4 m2;

L = 200 cm = 2 m

µr = 2000 ;

di = 20 – 0 = 20 A ;

dt = 0.02 s.

(i) Mutually inductance, M : 

Example 36. Two coils A and B are wound on the same ions core. There are 600 turns on A and 3000 turns on B. The current of 4 amperes through coil A produces a flux of 500 x 10-6 Wb in the core. If this current is reversed in 0.02 second, calculate average e.m.f. induced in coils A and B.

Solution. Given: N1 = 600;

N2 = 3600 ;

i1 = 4 A;

ɸ1 = 500 × 10-6 Wb ;

dt = 0.02 s.

E.m.f. induced in coils A and B, e1, e2:

Example 37. The coils A of 11450 turns and B of 14500 turns lie in parallel planes so that 65 per cent of flux produced in A links coil B. It is found that a current of 6 A in A produces a flux of 0.7 mWb while the same current in B produces 0.9 m Wb. Determine :

(i)           Mutual inductance;

(ii)         Co-efficient of coupling.

Solution. Given: N1, = 11450 ;

N2 = 14500 ;

ɸ2 = 0.65 ɸ1;

i1 = 6 A ;

ɸ1 = 0.7 m Wb = 0.7 × 10-3 Wb ;

ɸ2 = 0.9 m Wb = 0.9 × 10-3 Wb.

(i) Mutual inductance M:

Example 38. The combined inductance of two coils connected in series is 0.6 H or 0.1 H depending on the relative directions of the currents in the coils. If one of the coils when isolated has a self inductance of 0.2 h. Calculate:

(i)                           Mutual inductance ;

(ii)                        Coupling coefficient.

(Indore University)

Solution. (i) L = L1 + L2 + 2 M

or 0.6 = L1 + L2 + 2 M                                            … (i)

0.1=L1 + L2 - 2M                                                      … (ii)

From (i) and (ii), we get M = 0.125 H. (Ans.)

(ii) Let L1 = 0.2 H, then substituting this value in (i) above, we get L2 = 0.15 H