10. A cell of internal resistance 2 ohms supplies

Question

current to a 6-ohm resistor. The efficiency of the
cell is
A. 12.0 %
B. 25.0 %
C. 33.3 %
D. 75.0 %

Answer 1

To find the efficiency of the cell, we can use the formula:

Efficiency = (Power output / Power input) * 100%

Power output is the power dissipated in the 6-ohm resistor, which can be calculated using Ohm's Law:

Power output = I^2 * R

Power input is the power supplied by the cell, which can be calculated using the formula:

Power input = I^2 * (r + R)

where r is the internal resistance of the cell.

Given that the internal resistance is 2 ohms and the external resistance is 6 ohms, we can calculate the power output and power input:

Power output = I^2 * R = (I^2)(6)
Power input = I^2 * (r + R) = (I^2)(2 + 6)

To find the efficiency, we divide the power output by the power input and multiply by 100%:

Efficiency = [(I^2)(6) / (I^2)(2 + 6)] * 100%

Simplifying the equation:

Efficiency = (6 / 8) * 100%
Efficiency = 0.75 * 100%
Efficiency = 75%

Therefore, the efficiency of the cell is 75% or option D.