Voltage division insight: A series circuit has resistors of 4.7 kΩ, 12 kΩ, and 2.2 kΩ. Which resistor experiences the greatest voltage drop when powered by a DC source?

Introduction / Context:
In series networks, the supply voltage divides in proportion to resistance values. Identifying which component has the largest voltage drop helps with power rating choices and with understanding bias networks and sensor dividers.

Given Data / Assumptions:

• Three resistors in series: 4.7 kΩ, 12 kΩ, and 2.2 kΩ.
• Same current flows through each resistor (series circuit).
• DC, linear resistor behavior assumed.

Concept / Approach:
The drop across each resistor is V_i = I * R_i. Since the current I is identical for all three, the voltage drop is directly proportional to the resistance value. The largest resistance therefore drops the largest voltage.

Step-by-Step Solution:

Verification / Alternative check:
Pick a notional current (e.g., 1 mA). Then drops would be: 2.2 V, 4.7 V, and 12 V respectively, confirming the ranking with any positive current value.

Why Other Options Are Wrong:

• the 2.2 kΩ / the 4.7 kΩ: Smaller resistances produce proportionally smaller drops for the same current.
• impossible to determine: False; proportionality makes the determination straightforward without knowing the exact current.

Common Pitfalls:

• Assuming voltage divides equally; that only occurs when resistors are equal.
• Mixing series and parallel intuitions; in series, current is the same and voltage divides.

Final Answer:
the 12 kΩ