Physics Current Electricity UHS 2023
PMDC Verified Question 28 of 112
According to maximum power transfer theorem, which of the following is the max power delivered by the battery to the output?
A
\( E^2/4r \)
B
\( E^2/2r \)
C
\( E^2/5r \)
D
\( E^2/3r \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( E^2/4r \)
Concept:

Maximum power transfer occurs when the external load resistance (\(R\)) perfectly matches the internal resistance (\(r\)) of the source.

Formula:

$$ P = I^2 R \quad \text{and} \quad I = \frac{E}{R+r} $$

Solution:

  • For max power, set \( R = r \).


  • The current becomes \( I = \frac{E}{r + r} = \frac{E}{2r} \).


  • Substitute this current into the power formula: \( P_{max} = \left( \frac{E}{2r} \right)^2 \times r \).


  • \( P_{max} = \frac{E^2}{4r^2} \times r = \frac{E^2}{4r} \).


Why other options are incorrect:

  • Opt B, C, D: Mathematical errors from improper substitution or ignoring the squaring of the denominator \( 2r \).

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