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All resistors R1 through R6 of the circuit in figure 4 have the same resistance R. What is the power delivered by the batteries to resistor R6?

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Let loop currents be I1 and I2 as shown in the fig.. We write the loop equation for the upper loop using Kirchhoff's loop rule :

E2 - R3I1 - R6(I1 - I2) - E3 - R5(I1 - I2) - R4I1 = 0

Substituting R for all resistances :

E2 - RI1 - R(I1 - I2) - E3 - R(I1 - I2) - RI1 = 0

Or E2 - 4RI1 + 2RI2 - E3 = 0

Or 4RI1 - 2RI2 = E2 - E3 ........(1)

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