Physics
Physics
Problem
A student connects three resistors of , and in series across a battery and claims that the equivalent resistance of the combination is the average of the three resistances. Answer the following. a. (i) Explain, with reason, whether the student’s claim is correct or incorrect. b. (ii) Keeping the battery voltage unchanged, qualitatively describe how the current in the circuit would change if a fourth resistor is added in series. c. (iii) Distinguish between series and parallel connections with respect to how current divides or remains the same in the circuit.Intuitive explanation
The key insight here is understanding what "equivalent resistance" actually means in a series circuit. When resistors are in series, they don't average—instead, their resistances add directly because the same current flows through each one sequentially. The student's claim confuses the concept of averaging with how series circuits combine: the total resistance is the sum, not the mean. Once you find the true equivalent resistance, you can use Ohm's law to find the actual current and voltage drops, which will show why the student's reasoning leads to incorrect predictions about the circuit's behavior.
Intuitive explanation
The key insight here is understanding what "equivalent resistance" actually means in a series circuit. When resistors are in series, they don't average—instead, their resistances add directly because the same current flows through each one sequentially. The student's claim confuses the concept of averaging with how series circuits combine: the total resistance is the sum, not the mean. Once you find the true equivalent resistance, you can use Ohm's law to find the actual current and voltage drops, which will show why the student's reasoning leads to incorrect predictions about the circuit's behavior.