Question

The technician connects the lamp to a 6 V motorcycle battery instead of the 12 V car battery. He expects the current to be 400 mA (exactly ½ of the current 800 in the 12 V circuit). He measures the current and finds that it is not 400 mA. Explain why the current is not 400 mA.

Answer 1

The current is not 400 mA as expected because the motorcycle battery has a higher internal resistance than the car battery, thus supplying less current at the same voltage. Ohm's law dictates that the presence of higher internal resistance results in a reduced effective voltage across the lamp, leading to a smaller current.

Step-by-step explanation:

The technician observed that when connecting a lamp designed for a 12V battery to a 6V motorcycle battery, the expected current was not measured. The discrepancy suggests that the current does not scale linearly with voltage. This is because Ohm's law (V = IR) implies that the voltage across a resistor and the current through it are directly proportional if the resistance remains constant. In real-life applications, other factors like the internal resistance of the battery can influence current flow. A motorcycle battery has a higher internal resistance compared to a car battery, thus, for a given voltage, it would supply less current.

Also, using Ohm's Law, if the resistance remains constant and the voltage is halved (from 12V to 6V), the current should ideally be halved as well. However, the internal resistance eats up part of the voltage, leaving less voltage to drive the current through the lamp. The presence of internal resistance in the motorcycle battery means it cannot maintain the same voltage under load as the car battery. Hence, the smaller current observed in the 6V system as opposed to the predicted 400 mA is due to the higher internal resistance of the motorcycle battery resulting in a reduced effective voltage across the lamp.