Two different coils have $$self-inductance$$ $$L1=8mH$$, $$L2=2mH$$ . The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are $$i1$$, $$V1$$ and $$W1$$ respectively. Corresponding values for the second coil at the same instant are $$i2$$, $$V2$$ and $$W2$$ respectively. Then

Question

Two different coils have $$self-inductance$$  $$L1=8mH$$, $$L2=2mH$$ . The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are $$i1$$, $$V1$$ and $$W1$$ respectively. Corresponding values for the second coil at the same instant are $$i2$$, $$V2$$  and $$W2$$ respectively. Then

Infinity Learn · Accepted Answer

From Faraday’s Law, the induced voltage   V∝Lrate of change of current is constant   $$V=$$−Ldidt∴$$V2V1=L2L1=28=14$$⇒$$V1V2=4Power$$ given to the two coils is same, i.e., $$V1i1=V2i2$$⇒$$i1i2=V2V1=14Energy$$ stored  $$W=12Li2$$⇒$$W2W1=L2L1i2i12=14(4)2=4$$⇒$$W1W2=14$$

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