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The maximum power dissipated in an external resistance R, when connected to a cell of emf E and internal resistance r, will be ______.

Asked in GUJCET 2011 · Maximum power transfer

• (1) (E²)/r
• (2) (E²)/(2r)
• (3) (E²)/(3r)
• (4) (E²)/(4r)

Step-by-step solution

Why the other options are wrong

• (1) (E²)/r is the power the cell produces when shorted (R = 0, I = E/r). All of it is lost inside the cell; none reaches an external resistance.
• (2) (E²)/(2r) is the total power EI supplied by the cell when R = r (then I = E/(2r)). Half of it is lost in r; the external resistance receives (E²)/(4r).
• (3) No single slip gives (E²)/(3r). Sanity check: P = (E²R)/((R+r)²) never exceeds its value at R = r, which is (E²)/(4r).

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