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Q.

The inductors of two 𝐿𝑅 circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced 𝐸𝑀𝐹 in the inductors by the time the currents reach their steady state values is________ mJ.

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answer is 55.00.

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Detailed Solution

Mutual inductance is producing flux in same direction as self inductance.In steady state,I1=E1R1=55=1A I2=E2R2=2010=2Ae1=L1dI1dt+MdI2dte2=L2dI2dt+MdI1dt∴dW1+dW2=e1I1dt+e2I2dt⇒dW=L1I1dI1+L2I2dI2+MI1dI2+MI2dI1⇒dW=L1I1dI1+L2I2dI2+MdI1I2After integrating, ∴U=12L1I12+12L2I22+MI1I2⇒U=12×10×10−312+12×20×10−3×22+5×10−3×1×2 ⇒U=55mJ

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The inductors of two circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced in the inductors by the time the currents reach their steady state values is________ mJ.