If three different resistors are connected in series to a battery, which of the following statements is correct about the current through each resistor?

• A. The current is largest through the resistor with the smallest resistance.
• B. The current is zero through the resistor with the largest resistance.
• C. The current is different in each resistor depending on its resistance.
• D. The current is the same through all three resistors.

Answer: (D)

Verified step by step guidance

1. Recall the fundamental property of resistors connected in series: the same current flows through each resistor because there is only one path for the current to travel.
2. Understand that in a series circuit, the total resistance is the sum of the individual resistances, given by the formula \(R_{total} = R_1 + R_2 + R_3\).
3. Recognize that the current \(I\) in the circuit is determined by the total voltage \(V\) of the battery and the total resistance, using Ohm's law: \(I = \frac{V}{R_{total}}\).
4. Since the current is the same through each resistor, the voltage drop across each resistor can be different and is given by \(V_i = I \times R_i\), where \(R_i\) is the resistance of the individual resistor.
5. Conclude that the current does not depend on the individual resistances in a series circuit; it remains constant through all resistors, while the voltage divides according to the resistances.