A2L Item 242
- Description: Identify the circuit whose battery does more work establishing a current through an inductor.
- Goal: Reason regarding circuits
- Source: 283 Compare dissipated power with inductors
- Keywords: Inductors, Electromagnetism, Current, Circuits, Work
The question for students:
Consider the following circuits. Two identical batteries are connected to two identical inductors in series with different resistors. The switch is closed at t=0. Which is true regarding the energy supplied by the battery to establish current I?
- The battery in A does more work.
- The battery in B does more work.
- Both batteries do the same work.
- Cannot be determined
Commentary for teachers:
Answer
(4) It is not determined that either circuit can achieve the current I. If I is to be interpreted as the ‘final’ current, then the answer is #2. The lower the resistance the higher the final current. There is more energy stored in the inductor if the final current is higher. In addition, the energy dissipated in the resistor goes as i2R which is larger for circuit B for every current larger than V/(2R).