Question

)Two coils, X of 12000 turns and Y f 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5 A in X produces 0.05Wb while the same current in Y produces 0.075Wb. Calculate

Answer 1

Given that,

Number of turns of coil X = 12000 turns

Number of turns of coil Y = 1500 turns

Current in X = 5 A

Current in Y = 5 A

Flux in X = 0.05 Wb

Flux in Y = 0.075 Wb

Suppose, we need to calculate the mutual inductance,

Two coil lie in parallel plane and 45% of the flux produced by coil X links coil Y.

We know that,

The relation between induced emf and mutual inductance is

$\epsilon = M$

The relation between flux and mutual inductance is

$M=\dfrac{N\times \phi}{I}$

We need to calculate the mutual inductance

Using formula of mutual inductance

$M_{21}=\dfrac{N_{1}\times\phi_{1}}{I_{1}}$

Where, N = number of turns

$\phi$ = flux

I= current

Put the value into the formula

$M_{21}=\dfrac{1200\times0.45\times0.05}{5}$

$M_{21}=5.4$

$M_{21}=M_{12}=M=5.4\ Henry$

Hence, The mutual inductance is 5.4 Henry.