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Question

When $$100$$ volt dc is applied across a coil, a current of $$1amp$$ flows through it, when $$100volt$$ ac of $$50Hz$$ is applied to the same coild only $$0.5amp$$ flows. Calculate the resistance and inductance of the coil.


Solution

In case of a coil L-R circuit
$$I=\cfrac { V }{ Z } ,Z=\sqrt { { R }^{ 2 }+{ (\omega L) }^{ 2 } } $$
So when dc is applied, $$\omega =0,Z=R$$
And hence $$R=100\Omega $$
And when ac of $$50Hz$$ is applied
$$\quad I=\cfrac { V }{ Z } ,Z=\cfrac { V }{ I } =\cfrac { 100 }{ 0.5 } 200\Omega \quad $$
But $$Z=\sqrt { { R }^{ 2 }+{ (\omega L) }^{ 2 } } $$
$$2\pi f{ L }^{ 2 }={ 200 }^{ 2 }-{ 100 }^{ 2 }=3\times { 10 }^{ -4 }$$
$$\quad L=\cfrac { \sqrt { 3 } \times { 10 }^{ 2 } }{ 2\pi \times 50 } =\cfrac { \sqrt { 3 }  }{ \pi  } H=0.55H\quad $$

Physics

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