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, then total work done by the batteries against the induced πΈππΉ in the inductors by the time the currents reach their steady-state values is________mJ.
Step 1; Draw the required diagram:
Step 2: Given data:
Note that from the figure,
The resistance
The voltage
The value of inductances-
The value of mutual inductance
Step 3: Formula used:
The emf of LR circuit can be given as
Total work
Step 4: Calculate the total work:
Thus, using the above formula after integrating we get-
Therefore the total work
Now substitute the given values in the formula,
Therefore the total work
Therefore the total work is .