A battery has internal resistance r = 1 mΩ and provides a 2 A current to the circuit. If the terminal voltage is 3 V, what is the electromotive force of the battery?
a) 2 mV
b) 2.998 V
c) 3.002 V
d) 3.004 V
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Electromotive force of a battery is equal to terminal voltage plus Ir, or the product of the current and the battery’s own internal resistance. As the question states, the terminal voltage is 3 V, so choices A and B (both less than 3 V) must be wrong. The “Ir” term can simply be calculated by multiplying 2 A and 1 mΩ, or 2 A and 0.001 Ω. This yields 0.002 V, which (when added to 3 V) gives us 3.002 V.
a) This choice is just v = ir, the voltage to the circuit without terminal voltage.
b) This is the terminal voltage minus (not plus) the voltage to the circuit.
c) This correctly represents the terminal voltage plus the voltage to the circuit.
d) This is terminal voltage plus I2r (circuit power) rather than circuit voltage.