Question on: JAMB Physics - 2024
A cell of internal resistance of 2Ω supplies current through a resistor, X. If the efficiency of the cell is 75%, find the value of X.
A
2Ω
B
4Ω
C
6Ω
D
8Ω
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Correct Option: C
The efficiency of a cell is given by: Efficiency = (Output power / Input power) * 100%
The output power is the power dissipated in the external resistor (X), and the input power is the total power generated by the cell. Expressing efficiency in terms of resistance:
Efficiency = (X / (X + r)) * 100%
Where: X = external resistance, r = internal resistance
Given: Efficiency = 75%, r = 2 Ω
0.75 = X / (X + 2)
0.75 * (X + 2) = X → 0.75X + 1.5 = X → 1.5 = 0.25X → X = 6 Ω
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