A battery with EMF E and internal resistance r is connected across a resistance R. The power consumption in R will be maximum when :

### Related Formula P = I^2 R = left(fracER+rright)^2 R$$P = I^2 R = \left(\frac{E}{R+r}\right)^2 R$$ ### Core Logic To maximize power across the load resistance R$R$, we apply the Maximum Power Transfer Theorem. The power transferred to the load is maximum when the load resistance equals the internal resistance of the battery. Setting fracdPdR = 0$\frac{dP}{dR} = 0$ yields: R = r$R = r$ ### Step 1: Final Conclusion Power is maximum when the external resistance is strictly equal to the internal resistance (R=r$R=r$). ### Pattern Recognition Direct theoretical application of the Maximum Power Transfer Theorem. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Current Electricity