Explanation
1. Given Data
Electromotive force of the source (V) = 12 V
Internal resistance of the source (r) = 3Ω
Load resistance = R (variable)
2. Concept of Maximum Power Transfer Theorem
The Maximum Power Transfer Theorem states that a DC source delivers the maximum amount of power to a variable load resistance when the load resistance is exactly equal to the internal resistance of the source.
Therefore, for maximum power delivery:
R=r=3Ω
3. Derivation and Formula
The current (I) flowing through the simple series circuit is given by Ohm's Law:
I=R+rV
The power (P) dissipated across the load resistance R is:
P=I2R=(R+rV)2R
Substituting the condition for maximum power (R=r):
Pmax=(r+rV)2r=(2rV)2r=4r2V2×r
Pmax=4rV2
4. Step-by-Step Calculation
Now, substitute the given numerical values into the maximum power formula:
Pmax=4×3(12)2
Pmax=12144
Pmax=12 W
Correct Answer
The correct option is (c) 12 W.
