A 12.0 V battery is connected across a 4.00-Ω resistor. If the current through the resistor is 2.80 A, what is the internal resistance of the battery?
A) 0.200 Ω
B) 0.286 Ω
C) 4.29 Ω
D) 3.71 Ω
E) 0.800 Ω

Question

Quizplus · Accepted Answer

The internal resistance of the battery can be found using Ohm's law and the formula for total voltage in a circuit, which includes both the emf (electromotive force) of the battery and the voltage drop across the internal resistance. The total voltage (V) is the sum of the voltage across the external resistor (V_R) and the voltage across the internal resistance (V_r). Given that V = 12.0 V, I = 2.80 A, and R = 4.00 Ω, we first find V_R = I * R = 2.80 A * 4.00 Ω = 11.2 V. The difference between the battery voltage and V_R gives the voltage across the internal resistance, V_r = V - V_R = 12.0 V - 11.2 V = 0.8 V. The internal resistance (r) can then be found using Ohm's law, r = V_r / I = 0.8 V / 2.80 A = 0.286 Ω.

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